AFTER having furnished a ship with masts, yards, sails, blocks, anchors, &c. which are the requisites for putting to sea, it becomes no improper transition to pass thence to the use which is made of them in the working of ships; which, like all other sciences, consists of theory and practice. The knowledge of a theory, which is founded upon unerring principles, is surely indispensible for the correct attainment of the practice which it guides; and it cannot therefore be unuseful to shew that the theory of working ships is supported by mathematical principles, and capable of convincing demonstration.

M. Bourde de Villehuet, an officer in the service of the French East India Company, has been the most successful in explaining this theory, in his Le Manoeuvrier, published at Paris in 1769. He has, in that, improved upon the works of Pere Hoste, which were published above 100 years ago; and has clearly demonstrated his theory, without requiring such extent of geometrical knowledge as is necessary to the understanding of the elaborate treatise of M. Bouguer. To the theoretic part he has superadded directions for the performance of many evolutions; and has (which renders them particularly valuable) demonstrated the agreement of each with the mathematical principles he had before laid down. To have passed over a work of such character would have been highly blameable: we have therefore translated that part of M. Bourde's work; and we have incorporated with it directions for the performance of many operations which were unnoticed by that gentleman. The whole, we trust, will form the most extensive collection ever yet brought together; and all founded, we equally hope, upon the surest principles.

We do not affect to give specific directions for every possible situation of a ship at sea; because, if such directions could be given, they would most likely be unserviceable from their bulk: but, in explaining the theory upon which all maritime operations ought to be founded, we impart an unfailing source of knowledge to the seaman. Those principles will be his surest safeguard in the hour of danger, and his best assistant in the time of untried difficulty.

EXPLANATION OF THE TERMS USED IN SEAMANSHIP,

ABACK. The situation of the sails, when their surfaces are pressed aft against the mast by the force of the wind.

ABAFT. The hinder part of a ship, or towards the stern. It also signifies further aft or nearer to the stern; as, the barricade stands ABAFT the main mast; that is, nearer to the stern.

ABAFT THE BEAM denotes the relative situation of any object with the ship, when the object is placed in any part of that arch of the horizon which is contained between a line at right
angles with the keel and that point of the compass which is directly opposite to the ship's course.

ABOARD. The inside of a ship.

ABOARD MAIN TACK! The order to draw the lower corner of the mainsail down to the chess-tree.

ABOUT. The situation of a ship as soon as she has tacked or changed her course.

ABOUT SHIP! The order to the ship's crew to prepare for tacking.

ABREAST. The situation of two or more ships lying with their sides parallel, and their heads equally advanced; in which case, they are abreast of each other. But, if their sides be not parallel, then that ship, which is in a line with the beam of the other, is said to be abreast of her. With regard to objects within the ship, it implies on a line parallel with the beam, or at right angles with the ships length. ABREAST OF ANY PLACE, means off or directly opposite to it.

ADRIFT. The state of a ship broken from her moorings, and driving about without controul.

AFLOAT. Buoyed up by the water from the ground.

AFORE. All that part of a ship which lies forward, or near the stem. It also signifies further forward; as, the manger stands AFORE the fore mast; that is, nearer to the stem.

AFT. Behind, or near the stern of the ship.

AFTER. A phrase applied to any object in the hinder part of the ship, as the after-hatchway, the after-sails, &c.

A-GROUND. The situation of a ship when her bottom or any part of it rests on the ground.

A-HEAD. Any thing which is situated on that point of the compass to which a ship's stem is directed, is said to be a-head of her.

A-HULL. The situation of a ship, when all her sails are furled and her helm is lashed to the lee side; by which she lies nearly with her side to the wind and sea, her head being somewhat inclined to the direction of the wind.

A-LEE. The position of the helm when it is pushed down to the lee side.

ALL IN THE WIND. The state of a ship's sails, when they are parallel to the direction of the wind, so as to shake or shiver.

ALL HANDS HOAY! The call by which all the ship's company are summoned upon deck,

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ALOFT. Up in the tops, at the mast-heads, or any where about the higher rigging.

ALONG-SIDE. Side-by-side, or joined to a ship, wharf, &c.

ALONG-SHORE. Along the coast; a course which is in sight of the shore, and nearly parallel to it.

AMAIN. At once, suddenly: as LET GO AMAIN!

AMIDSHIPS. The middle of a ship, either with regard to her length or breadth.

To ANCHOR. To let the anchor fall into the ground, for the ship to ride thereby.

ANCHORAGE. Ground, fit to hold a ship by her anchor.

THE ANCHOR IS A COCK-BILL. The situation of the anchor, when it drops down perpendicularly from the cat-head, ready to be sunk at a moment's warning.

AN-END. The position of any mast, &c. when erected perpendicularly on the deck. The top-masts are said to be AN-END, when they are hoisted up to their usual stations.

APEEK. Perpendicular to the anchor; the cable having been drawn so tight as to bring the ship directly over it. The anchor is then said to be APEEK.

ASHORE. On the shore, as opposed to ABOARD. It also means AGROUND.

ASTERN. Any distance behind a ship, as opposed to A-HEAD.

AT ANCHOR. The situation of a ship riding by her anchor.

ATHWART. Across the line of a ship's course.

ATHWART-HAWSE. The situation of a ship when driven by accident across the fore-part of another, whether they touch or are at a small distance from each other, the transverse position of the former being principally understood.

ATHWART THE FORE FOOT denotes the flight of a cannon-ball fired from one ship across the line of another's course, but a-head of her.

ATHWART-SHIPS. Reaching, or in a direction, across the ship from one side to the other.

ATRIP. When applied to the anchor, it means that the anchor is drawn out of the ground,
and hangs in a perpendicular direction, by the cable or buoy-rope. The topsails are said to be ATRIP, when they are hoisted up to the mast-head, or to their utmost extent.

AVAST! The command to stop, or cease, in any operation.

AWEIGH. The same as ATRIP, when applied to the anchor.

To BACK THE ANCHOR. To carry out a small anchor a-head of the large one, in order to support it in bad ground, and to prevent it from loosening or coming home.

To BACK ASTERN, in rowing, is to impel the boat with her stern foremost, by means of the oars.

To BACK THE SAILS. To arrange them in a situation that will occasion the ship to move a-stern.

To BAGPIPE THE MIZEN. To lay it aback, by bringing the sheet to the mizen shrouds.

To BALANCE. To contract a sail into a narrower compass, by folding up a part of it at one
corner. BALANCING is peculiar only to the mizen of a ship, and the mainsail of those vessels wherein
it is extended by a boom.

BARE POLES. When a ship has no sail set, she is UNDER BARE POLES.

BEARING. The situation of one place from another, with regard to the points of the compass. The situation also of any distant object, estimated from some part of the ship, according to
her situation: these latter bearings are either ON THE BEAM; BEFORE THE BEAM; ABAFT THE BEAM;
ON THE LEE OR WEATHER BOW; ON THE LEE OR WEATHER QUARTER; A-HEAD; OR A-STERN.

BEAR A-HAND. Make haste, dispatch.

To BEAR IN WITH THE LAND is when a ship sails towards the shore.

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To BEAR OFF. To thrust or keep off from the ship's side, &c. any weight, when hoisting.

To BEAR UP, OR AWAY. The act of changing a ships course, to make her sail more before the wind.

BEATING TO WINDWARD. The making a progress at sea against the direction of the wind, by steering alternately close-hauled on the starboard and larboard tacks.

To BECALM. To intercept the current of the wind, in its passage to a ship, by any contiguous object, as a shore above her sails, a high sea behind, &c. and thus one sail is said to becalm another.

BEFORE THE BEAM denotes an arch of the horizon comprehended between the line of the beam and that point of the compass on which the ship stems.

To BELAY. To fasten a rope, by winding it several times round a cleat or pin.

To BEND A SAIL is to affix it to its proper yard or stay.

BENEAPED. See NEAPED.

BETWEEN-DECKS. The space contained between any two decks of a ship.

BILGE-WATER is that which, by reason of the flatness of a ship's bottom, lies on her floor, and cannot go to the well of the pump.

BIRTH. The station in which a ship rides at anchor, either alone or in a fleet; the due distance between two ships; and also a room or apartment on board for the officers of a mess.

To BITT THE CABLE is to confine the cable to the bitts, by one turn under the cross-piece and another turn round the bitt-head. In this position it may be either kept fixed, or it may be veered away.

BITTER. The turn of the cable round the bitts.

BITTER-END. That part of the cable which stays within-board round about the bitts when the ship is at anchor.

A BOARD is the distance run by a ship on one tack; thus they say, a good board, when a ship does not go to leeward of her course; a short board and a long board, according to the distance run.

BOARD-AND-BOARD. When two ships come so near as to touch each other, or when they lie side-by-side.

To BOARD A SHIP. To enter an enemy's ship in an engagement.

BOLD SHORE. A steep coast, permitting the close approach of shipping.

BOOT-TOPPING. Cleaning the upper part of a ship's bottom, or that part which lies immediately under the surface of the water; and daubing it over with tallow, or with a mixture of tallow, sulphur, rosin, &c.

BOTH SHEETS AFT. The situation of a ship sailing right before the wind.

BOW-GRACE. A frame of old rope or junk, laid out at the bows, stems, and sides, of ships, to prevent them from being injured by flakes of ice.

To BOWSE. To pull upon any body with a tackle, in order to remove it.

BOXHAULING. A particular method of veering a ship, when the swell of the sea renders tacking impracticable.

BOXING. An operation somewhat similar to BOXHAULING. It is performed by laying the headsails aback, to receive the greatest force of the wind in a line perpendicular to their surfaces, in order
to return the ship's head into the line of her course, after she had inclined to windward of it.

To BRACE THE YARDS. To move the yards, by means of the braces, to any direction required.

To BRACE ABOUT. To brace the yards round for the contrary tack.

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To BRACE SHARP. To brace the yards to a position, in which they will make the smallest possible angle with the keel, for the ship to have head-way.

To BRACE-TO. To ease off the lee-braces, and round-in the weather braces, to assist the motion of the ship's head in tacking.

To BRAIL UP. To haul up a sail by means of the brails, for the more readily furling it when necessary.

BRAILS. A name peculiar only to certain ropes belonging to the mizen, used to truss it up to the mast. But it is likewise applied to all the ropes, which are employed in hauling up the bottoms, lower corners, and skirts, of the other great sails.

To BREAK BULK. The act of beginning to unload a ship.

To BREAK SHEER. When a ship at anchor is forced, by the wind or current, from that position in which he keeps her anchor most free of herself and most firm in the ground, so as to endanger the tripping of her anchor, she is said to break her sheer.

BREAMING. Burning off the filth from a ship's bottom.

BREAST-FAST. A rope employed to confine a ship sideways to a wharf, or to some other ship.

To BRING BY THE LEE. See TO BROACH-TO.

To BRING-TO. To check the course of a ship when she is advancing, by arranging the sails in such a manner as that they shall counteract each other, and prevent her from either retreating or advancing.

To BROACH-TO. To incline suddenly to windward of the ship's course, so as to present her side to the wind, and endanger her oversetting. The difference between BROACHING-TO and BRINGING BY THE LEE may be thus defined. Suppose a ship under great sail is steering South, having the wind at N N W; then West is the weather-side, and East the lee side. If, by any accident, her head turns round to the westward, so as that her sails are all taken a-back on the weather-side, she is said to BROACH-TO. If, on the contrary, her head declines so far eastward as to lay her sails a-back on that side which was the lee-side, it is called BRINGING BY THE LEE.

BROADSIDE. A discharge of all the guns on one side of a ship, both above and below.

BROKEN-BACKED. The state of a ship which is so loosened in her frame, as to drop at each end.

BY THE BOARD. Over the ship's side.

BY THE HEAD. The state of a ship when drawing more water forward than a-stern.

BY THE WIND. The course of a ship as near as possible to the direction of the wind, which is generally within six points of it.

To CAREEN. To incline a ship on one side so low down, by the application of a strong purchase
to her masts, as that her bottom on the other side, may be cleansed by breaming.

CASTING. The motion of falling-off, so as to bring the direction of the wind on either side
of the ship, after it had blown some time right a-head. It is particularly applied to a ship about
to weigh anchor.

To CAT THE ANCHOR is to hook the cat-block to the ring of the anchor, and haul it up close to the cat-head.

CAT's-PAW. A light air of wind perceived at a distance in a calm, sweeping the surface of the sea very lightly, and dying away before it reaches the ship.

CENTER. This word is applied to that squadron of a fleet, in line of battle, which occupies the middle of the line; and to that column (in the order of sailing) which is between the weather and lee columns.

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CHANGE THE MIZEN. Bring the mizen yard over to the other side of the mast.

CHAPPELLING. The act of turning a ship round in a light breeze of wind when she is close-hauled, so as that she will lie the same way she did before. This is usually occasioned by negligence in steering, or by a sudden change of wind.

CHASE. A vessel pursued by some other.

CHASER. The vessel pursuing.

CHEERLY. A phrase implying heartily, quickly, cheerfully.

To CLAW OFF. The act of turning to windward from a lee-shore, to escape shipwreck, &c.

CLEAR is variously applied. The weather is said to be CLEAR, when it is fair and open; the sea-coast is CLEAR, when the navigation is not interrupted by rocks, &c. it is applied to cordage, cables, &c. when they are disentangled, so as to be ready for immediate service. In all these senses it is opposed to FOUL.

To CLEAR THE ANCHOR is to get the cable off the flukes, and to disencumber it of ropes ready for dropping.

CLEAR HAWSE. When the cables are directed to their anchors without lying athwart the stem.

To CLEAR THE HAWSE is to untwist the cables when they are entangled by having either a cross, an elbow, or a round turn.

CLENCHED. Made fast, as the cable is to the ring of the anchor.

CLOSE-HAULED. That trim of the ship's sails, when she endeavours to make a progress in the nearest direction possible towards that point of the compass from which the wind blows.

To CLUB-HAUL. A method of tacking a ship when it is expected she will miss stays on a lee-shore.

To CLUE-UP. To haul up the clues of a sail to its yard, by means of the clue-lines.

COASTING. The act of making a progress along the sea-coast of any country.

To COIL THE CABLE. To lay it round in a ring, one turn over another.

To COME HOME. The anchor is said to come home, when it loosens from the ground by the
effort of the cable, and approaches the place where the ship floated, at the length of her moorings.

COMING-TO denotes the approach of a ship's head to the direction of the wind.

COURSE. The point of the compass on which a ship steers.

CRANK. The quality of a ship, which, for want of sufficient ballast, is rendered incapable of carrying sail without being exposed to the danger of oversetting.

To CROWD SAIL. To carry more sail than ordinary.

CUNNING. The art of directing the steersman to guide the ship in her proper course.

To CUT AND RUN. To cut the cable and make sail instantly, without waiting to weigh anchor.

To DEADEN A SHIP'S WAY. To impede her progress through the water.

DEAD-WATER. The eddy of water, which appears like whirl-pools, closing in with the ship's stern as the sails on.

DISMASTED. The state of a ship that has lost her masts.

DOUBLING. The act of sailing round, or passing beyond a cape or point of land.

DOUBLING-UPON The act of inclosing any part of a hostile fleet between two fires, or of cannonading it on both sides.

To DOWSE. To lower suddenly, or slacken.

To DRAG THE ANCHOR. To trail it along the bottom, after it is loosened from the ground.

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To DRAW. When a sail is inflated by the wind, so as to advance the vessel in her course, the sail is said TO DRAW; and so, TO KEEP ALL DRAWING is to inflate all the sails.

DRIFT. The angle which the line of a ship's motion makes with the nearest meridian, when she drives with her side to the wind and waves, and not governed by the power of the helm. It also implies the distance which the ship drives on that line.

DRIVING. The state of being carried at random, as impelled by a storm or current. It is
generally expressed of a ship, when accidentally broke loose from her anchors or moorings.

DROP. Used sometimes to denote the depth of a sail; as, the fore topsail DROPS twelve yards.

To DROP ANCHOR. Used synonymously with TO ANCHOR.

To DROP A-STERN. The retrograde motion of a ship.

To EASE, TO EASE AWAY, OR TO EASE OFF. To slacken gradually, thus they say, EASE the bowline, EASE the sheet.

EASE THE SHIP! The command given by the pilot to the steersman, to put the helm hard
a-lee, when the ship is expected to plunge her fore part deep in the water, when close-hauled.

To EDGE AWAY. To decline gradually from the shore, or from the line of the course which
the ship formerly held, in order to go more large.

To EDGE IN WITH. To advance gradually towards the shore or any other object.

ELBOW IN THE HAWSE. A particular twist in the cables by which a ship is moored; explained at length hereafter in the PRACTICE OF WORKING SHIPS.

END-FOR-END. A reversal of the position of any thing is turning it END-FOR-END. It is applied also to a rope that has run quite out of the block in which it was reeved; or to a cable which has all run out of the ship.

END-ON. When a ship advances to a shore, rock, &c. without an apparent possibility of preventing her, she is said to go END-ON for the shore, &c.

EVEN-KEEL. When the keel is parallel with the horizon, a ship is said to be upon an EVEN-KEEL.

FAIR. A general term for the disposition of the wind when favourable to a ship's course.

FAIR-WAY. The channel of a narrow bay, river, or haven, in which ships usually advance in their passage up and down.

To FALL A-BOARD OF. To strike or encounter another ship, when one or both are in motion.

To FALL A-STERN. The motion of a ship with her stern foremost.

To FALL CALM. To become in a state of rest by a total cessation of the wind.

To FALL DOWN. To sail or be towed down a river nearer towards its mouth.

FALLING-OFF denotes the motion of the ship's head from the direction of the wind.

FALL NOT OFF! The command to the steersman to keep the ship near the wind.

To FETCH WAY. To be shaken or agitated from one side to another so as to loosen any
thing which was before fixed.

To FILL. To brace the sails so as to receive the wind in them, and advance the ship in her course, after they had been either shivering or braced a-back.

To FISH THE ANCHOR. To draw up the flukes of the anchor towards the top of the bow, in order to stow it, after having been catted.

FLAT-AFT. The situation of the sails when their surfaces are pressed aft against the mast by the force of the wind.

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To FLAT-IN. To draw in the aftermost lower corner or clue of a sail towards the middle of the ship, to give the sail a greater power to turn the vessel.

To FLAT-IN FORWARD. To draw in the fore sheet, jib sheet, and fore staysail-sheet towards the middle of the ship.

FLAW. A sudden breeze or gust of wind.

FLOATING. The state of being buoyed up by the water from the ground.

FLOOD-TIDE. The state of a tide when it flows or rises.

FLOWING SHEETS. The position of the sheets of the principal sails when they are loosened to the wind, so as to receive it into their cavities more nearly perpendicular than when close-hauled, but more obliquely than when the ship sails before the wind. A ship going two or three points large
has FLOWING SHEETS.

FORE. That part of a ship's frame and machinery that lies near the stem.

FORE-AND-AFT. Throughout the whole ship's length. Lengthways of the ship.

To FORE-REACH UPON. To gain ground of some other ship.

To FORGE OVER. To force a ship violently over a shoal, by a great quantity of sail.

FORWARD. Towards the fore part of a ship.

FOUL. Is used in opposition both to CLEAR and FAIR. As opposed to clear, we say FOUL,
WEATHER; FOUL BOTTOM; FOUL GROUND; FOUL ANCHOR; FOUL HAWSE. As opposed to fair, we say FOUL WIND.

To FOUNDER. To sink at sea, by filling with water.

To FREE. Pumping is said to FREE the ship when it discharges more water than leaks into her.

To FRESHEN. When a gale increases it is said TO FRESHEN.

To FRESHEN THE HAWSE. Veering out or heaving in a little cable, to let another part of it endure the stress at the hawse-holes. It is also applied to the act of renewing the service round the cable at the hawse-holes.

FRESH WAY. When a ship increases her velocity she is laid to get FRESH WAY.

FULL. The situation of the sails, when they are kept distended by the wind.

FULL-AND-BY. The situation of a ship, with regard to the wind, when close-hauled; and
sailing, so as to steer neither too nigh the direction nor to deviate to leeward.

To FURL. To wrap or roll a sail close up to the yard or stay to which it belongs, and winding a cord round it, to keep it fast.

To GAIN THE WIND. To arrive on the weather-side, or to windward of, some ship or fleet in sight, when both are sailing as near the wind as possible.

To GATHER. A ship is said to GATHER on another, as she comes nearer to her.

GIMBLETING. The action of turning the anchor round by the stock, so that the motion of
stock appears similar to that of the handle of a gimblet, when employed to turn the wire.

To GIVE CHASE TO. To pursue a ship or fleet.

GOOSE-WINGS OF A SAIL. The clues or lower corners of a ship's mainsail or foresail, when the middle part is furled or tied up to the yard.

GRIPING. The inclination of a ship to run to windward of her proper course.

GROUNDING. The laying a ship a-shore, in order to repair her. It is also applied to running a-ground accidentally.

GROUND-TACKLE. Every thing belonging to a ship's anchors, and which are necessary for anchoring or mooring; such as cables, hawsers, tow-lines, warps, buoy-ropes, &c.

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GROWING. Stretching out; applied to the direction of the cable from the ship towards the anchors; as, the cable GROWS on the starboard bow.

GYBING. The act of shifting any boom-sail from one side of the mast to the other.

To HAIL. To salute or speak to a ship at a distance.

To HAND THE SAILS. The same as to FURL them.

HAND-OVER-HAND. The pulling of any rope, by the men's passing their hands alternately
one before the other or one above another. A sailor is said to go aloft
HAND-OVER-HAND when he
climbs into the tops by a single rope, dexterously throwing one hand over the other.

HANDSOMELY. Gradually, as LOWER HANDSOMELY.

HANK-FOR-HANK. When two ships tack and make a progress to windward together.

HARD A-LEE. The situation of the helm, when pushed close to the lee side of the ship.

HARD A-WEATHER. The situation of the helm, when pushed close to the weather side of
the ship.

To HAUL. To pull a single rope without the assistance of blocks.

To HAUL THE WIND. To direct the ship's course nearer to the point from which the wind blows.

HAWSE. The situation of the cables before the ship's stem, when she is moored with two anchors out from forward. It also denotes any small distance a-head of a ship, or the space between her head and the anchors employed to ride her.

HEAD-FAST. A rope employed to confine the head of a ship to a wharf or to some other ship.

HEADMOST. The situation of any ship or ships which are the most advanced in a fleet.

HEAD-SAILS. All the sails which belong to the fore-mast and bowsprit.

HEAD-SEA. When the waves meet the head of a ship in her course, they are called a HEAD-SEA. It is likewise applied to a large single wave coming in that direction.

HEAD-TO-WIND. The situation of a ship when her head is turned to the point from which the wind blows.

HEAD-WAY. The motion of advancing at sea.

To HEAVE. To turn about a capstern, or other machine of the like kind, by means of bars, handspecs, &c.

To HEAVE A-HEAD. To advance the ship by heaving-in the cable or other rope fastened to an anchor at some distance before her.

To HEAVE A-PEEK. To heave-in the cable, till the anchor is a-peek.

To HEAVE A-STERN. To move a ship backwards by an operation similar to that of HEAVING A-HEAD.

To HEAVE DOWN. To CAREEN.

To HEAVE-IN THE CABLE. To draw the cable into the ship, by turning the capstern.

To HEAVE IN STAYS. To bring a ship's head to the wind, by a management of the sails and rudder, in order to get on the other tack.

To HEAVE OUT. To unfurl or loose a sail; more particularly applied to the staysails: thus we say, loose the topsails and HEAVE OUT the staysails.

To HEAVE SHORT. To draw so much of the cable into the ship, as that she will be almost perpendicularly over her anchor.

To HEAVE TIGHT or TAUGHT. To turn the capstern round, till the rope or cable becomes straitened.

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To HEAVE THE CAPSTERN. To turn it round.

To HEAVE THE LEAD. To throw the lead overboard, in order to find the depth of water.

To HEAVE THE LOG. To throw the log overboard, in order to calculate the velocity of the ship's
way.

To HEEL. To stoop or incline to one side; thus they say TO HEEL TO PORT, that is, to heel to the larboard side.

HELM A-LEE! A direction to put the helm over to the lee side.

HELM A-WEATHER! An order to put the helm over to the windward side.

HIGH-AND-DRY. The situation of a ship when so far run aground as to be seen dry upon the strand.

To HOIST. To draw up any body by the assistance of one or more tackles. Pulling by means of a single block is never termed HOISTING, except only the drawing of the sails upwards along the masts or stays.

To HOLD ITS OWN is applied to the relative situation of two ships when neither advances upon the other; each is then said to HOLD ITS OWN. It is likewise said of a ship which, by means of contrary winds, cannot make a progress towards her destined port, but which however keeps nearly the distance she had already run.

To HOLD ON. To pull back or retain any quantity of rope acquired by the effort of a capstern, windlass, tackle, block, &c.

HOME implies the proper situation of any object; as, to haul HOME the topsail sheets is to extend the bottom of the topsail to the lower yard, by means of the sheets. In stowing a hold, a cask, &c. is said to be HOME, when it lies close to some other object.

To HULL A 8HIP. To fire cannot balls into her hull within the point-blank range.

HULL-TO. The situation of a ship when she lies with all her sails furled; as in TRYING.

IN STAYS. See TO HEAVE in stays.

KECKLED. Any part of a cable, covered over with old ropes, to preserve its surface from rubbing against the ship's bow or fore foot.

To KEEP AWAY. To alter the ship's course to one rather more large, for a little time, to avoid some ship, danger, &c. KEEP AWAY is likewise said to the steersman, who is apt to go to windward of the ship's course.

To KEEP FULL. To keep the sails distended by the wind.

To KEEP HOLD OF THE LAND. To steer near to or in sight of the land.

To KEEP OFF. To sail off or keep at a distance from the shore.

To KEEP THE LAND A-BOARD. The same as To KEEP HOLD OF THE LAND.

To KEEP THE LUFF. To continue close to the wind.

To KEEP THE WIND. The same as TO KEEP THE LUFF.

KNOT. A division of the log-line, answering, in the calculation of the ship's velocity, to one mile.

To LABOUR. To roll or pitch heavily in a turbulent sea.

LADEN IN BULK. Freighted with a cargo not packed, but lying loose, as corn, salt, &c.

LAID-UP. The situation of a ship when moored in a harbour, for want of employ.

LAND-FALL. The first land discovered after a sea-voyage. Thus a GOOD LAND FALL implies
the land expected or desired; a BAD LAND-FALL the reverse.

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LAND-LOCKED. The situation of a ship surrounded with land, so as to exclude the prospect of the sea, unless over some intervening land.

LARBOARD. The left side of a ship, looking towards the head.

LARBOARD-TACK. The situation of a ship when sailing with the wind blowing upon her larboard side.

LAYING THE LAND. The motion of a ship which increases her distance from the coast, so as to make it appear lower and smaller.

LEADING-WIND: A fair wind for a ship's course.

LEAK. A chink or breach in the sides or bottom of a ship, through which the water enters into the hull.

To LEAK. To admit water into the hull through chinks or breaches in the sides or bottom.

LEE. That part of the hemisphere to which the wind is directed, to distinguish it from the other part which is called to windward.

LEE-GAGE. A ship or fleet to leeward of another is said to have the lee-gage.

LEE-LURCHES. The sudden and violent rolls which a ship often takes to leeward, in a high sea; particularly when a large wave strikes her on the weather side.

LEE OF THE SHORE. See UNDER THE LEE OF THE SHORE.

LEE-QUARTER. That quarter of a ship which is on the lee side.

LEE-SHORE. That shore upon which the wind blows.

LEE SIDE. That half of a ship lengthwise, which lies between a line drawn through the middle of her length and the side which is furthest from the point of the wind.

To LEEWARD. Towards that part of the horizon to which the wind blows.

LEEWARD SHIP. A ship that falls much to leeward of her course, when sailing close-hauled.

LEEWARD TIDE. A tide that sets to leeward.

LEE WAY. The lateral movement of a ship to leeward of her course; or the angle which the line of her way makes with a line in the direction of her keel.

To LIE ALONG. To be pressed down sideways by a weight of sail, in a fresh wind.

To LIE-TO. To retard a ship in her course, by arranging the sails in such a manner as to counteract each other with nearly an equal effort, and render the ship almost immoveable, with respect to her
progressive motion or headway.

A LONG SEA. An uniform motion of long waves.

LOOK-OUT. A watchful attention to some important object or event that is expected to arise.

To LOOSE. To unfurl or cast loose any sail.

To LOWER. To ease down gradually.

LUFF! The order to the steersman to put the helm towards the lee side of the ship, in order to sail nearer to the wind.

To MAKE A BOARD. To run a certain distance upon one tack, in beating to windward.

To MAKE FOUL WATER. To muddy the water, by running in shallow places, so that the ship's keel disturbs the mud at bottom.

To MAKE SAIL. To increase the quantity of sail already set, either by unreefing or by setting others.

To MAKE STERNWAY. To retreat or move with the stern foremost.

To MAKE THE LAND. To discover it from afar.

To MAKE WATER. To leak.

To MAN THE YARD, &c. To place men on the yard, in the tops, down the ladder, &c. to execute any necessary duties.

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MASTED. Having all her masts complete.

To MIDDLE A ROPE. To double it into two equal parts.

MIDSHIPS. See AMIDSHIPS.

To MISS STAYS. A ship is said to MISS STAYS, when her head will not fly up into the direction of the wind, in order to get her on the other tack.

MOORING. Securing a ship in a particular station by chains or cables, which are either fastened to an adjacent shore or to anchors at the bottom.

MOORING SERVICE. When a ship is moored, and rides at one cable's length, the mooring service is that which is at the first splice.

NEAPED. The situation of a ship left aground on the height of a spring tide, so that she cannot be floated till the return of the next spring tide.

NEAR or NO NEAR. An order to the steersman not to keep the ship so close to the wind.

OFF-AND-ON. When a ship is beating to windward, so that by one board she approaches towards the shore, and by the other stands out to sea, she is said to stand OFF-AND-ON shore.

OFFING. Out at sea, or at a competent distance from the shore, and generally out of anchor ground.

OFFWARD. From the shore; as when a ship lies aground and leans towards the sea, she is said
to heel OFFWARD.

ON THE BEAM. Any distance from the ship on a line with the beams, or at right angles with the keel.

ON THE BOW. An arch of the horizon, comprehending about four points of the compass on each
side of that point to which the ship's head is directed. Thus, they say, the ship in sight bears three
points ON THE STARBOARD-BOW; that is, three points, towards the right-hand, from that part of the horizon which is right a-head.

ON THE QUARTER. An arch of the horizon, comprehending about four points of the compass on each side of that point to which the ship's stern is directed. See ON THE BOW.

OPEN. The situation of a place exposed to the wind and sea. It is also expressed of any distant object to which the sight or passage is not intercepted.

OPEN HAWSE. When a ship at her moorings has her cables lead strait to her anchors, without crossing, she is said to ride with an OPEN HAWSE.

OVER-BOARD. Out of the ship.

OVER-GROWN SEA is expressed of the ocean when the surges and billows rise extremely high.

To OVER-HAUL. To open and extend the several parts of a tackle, or other assemblage of ropes, thereby fitting them the better for running easily.

OVER-RAKE. When a ship at anchor is exposed to a head-sea, the waves of which break in upon her, the waves are laid to OVER-RAKE her.

OVER-SET. A ship is OVER-SET, when her keel turns upwards.

OUT-OF-TRIM. The state of a ship, when she is not properly balanced for the purposes of navigation.

PARLIAMENT-HEEL. The situation of a ship when she is made to stoop a little to one side, so as to clean the upper part of her bottom on the other side. See BOOT-TOPPING.

PARTING. Being driven from the anchors, by the breaking of the cable.

To PAWL THE CAPSTERN. To fix the pawls, so as to prevent the capstern from recoiling, during any pause of heaving.

To PAY. To daub or cover the surface of any body, in order to preserve it from the injuries of the weather, &c.

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To PAY AWAY or PAY OUT. To slacken a cable or other rope, so as to let it run out for some particular purpose.

To PAY OFF. To move a ship's head to leeward.

To PEEK THE MIZEN. To put the mizen-yard perpendicular by the mast.

PITCHING. The movement of a ship, by which she plunges her head and after-part alternately into the hollow of the sea.

To PLY To WINDWARD. To endeavour to make a progress against the direction of the wind. See BEATING To WINDWARD.

POINT-BLANK. The direction of a gun when levelled horizontally.

POOPING. The shock of a high and heavy sea upon the stern or quarter of a ship, when she scuds before the wind in a tempest.

PORT. A name given on some occasions to the larboard side of the ship as, the ship heels to port, top the yards to port, &c.

PORT THE HELM. The order to put the helm over to the larboard side.

PORT-LAST. The gunwale.

PORTOISE. The same as PORT-LAST; TO RIDE A PORTOISE is to ride with a yard struck down to the deck.

PRESS OF SAIL. All the sail a ship can set or carry.

PRIZING. The application of a lever to move any weighty body.

PURCHASE. Any sort of mechanical power employed in raising or removing heavy bodies.

QUARTERS. The several stations of a ship's crew in time of action.

QUARTERING. When a ship under sail has the wind blowing on her quarter.

To RAISE. To elevate any distant object at sea by approaching it; thus, TO RAISE THE LAND is used in opposition to LAY THE LAND.

To RAKE. To cannonade a ship at the stern or head, so that the balls scour the whole length of the decks.

RANGE. A sufficient length of cable drawn upon deck before the anchor is cast loose, to admit of its sinking to the bottom, without any check.

REACH. The distance between any two points on the banks of a river, wherein the current flows in an uninterrupted course.

READY ABOUT! A command of the boatswain to the crew, and implies that all the hands are to be attentive, and at their stations for tacking.

REAR. The last division of a squadron, or the last squadron of a fleet. It is applied likewise to the last ship of a line, squadron, or division.

REEF. Part of a sail from one row of eyelet-holes to another. It is applied likewise to a chain of rocks lying near the surface of the water.

REEFING. The operation of reducing a sail, by taking in one or more of the reefs.

To REEVE. To pass the end of a rope through any hole, as the channel of a block, the cavity of a thimble, &c.

RENDERING. The giving way or yielding to the efforts of some mechanical power. It is used in opposition to jambing or sticking.

RIDING, when expressed of a ship, is the state of being retained in a particular station, by an anchor and cable: thus she is said to RIDE EASY or to RIDE HARD, in proportion to the strain upon her cable. She is likewise said to RIDE LEEWARD TIDE, if anchored in a place at a time when the tide sets to leeward; and to RIDE WINDWARD TIDE, if the tide sets to windward: to RIDE BETWEEN

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WIND AND TIDE, when the wind and tide are in direct opposition, causing her to ride without
any strain upon her cables.

RIGHTING. Restoring a ship to an upright position, either after she has been laid on a careen,
or after she has been pressed down on her side by the wind.

To RIGHT THE HELM is to bring it into midships, after it has been pushed either to starboard or
larboard.

RIGGING OUT A BOOM. The running out a pole at the end of a yard, to extend the foot of
a sail.

To RIG THE CAPSTERN. To fix the bars in their respective holes.

ROLLING. The motion by which a ship rocks from side to side like a cradle.

ROUGH-TREE. A name applied to any mast, yard, or boom, placed in merchant ships, as a
rail or fence above the vessel's side, from the quarter-deck to the forecastle.

ROUNDING-IN. The pulling upon any rope which passes through one or more blocks in a
direction nearly horizontal; as, ROUND-IN the weather braces.

ROUND-TURN. The situation of the two cables of a ship when moored, after they have been
several times crossed by the swinging of the ship.

ROUNDING-UP. Similar to ROUNDING-IN, except that it is applied to ropes and blocks which
act in a perpendicular direction.

To ROW. To move a boat with oars.

ROWSING. Pulling upon a cable or rope, without the assistance of tackles.

To RUN OUT A WARP. To carry the end of a rope out from a ship, in a boat, and fastening it to some distant object; so that by it the ship may be removed by pulling on it.

To SAG To LEEWARD. To make considerable lee-way.

SAILING-TRIM is expressed of a ship when in the best state for sailing.

SCANTING. The variation of the wind, by which it becomes unfavourable to a ship's making great progress, as it deviates from being large, and obliges the vessel to steer close-hauled or nearly so.

SCUDDING. The movement by which a ship is carried precipitately before the wind in a tempest.

SCUTTLING. Cutting large holes through the bottom or sides of a ship, either to sink her, or to unlade her expeditiously when stranded.

SEA. A large wave is so called; thus they say, a HEAVY SEA. It implies, likewise, the agitation of the ocean, as, a GREAT SEA. It expresses the direction of the waves, as, a HEAD-SEA. A LONG
SEA means an uniform and steady motion of long and extensive waves; a SHORT SEA, on the contrary, is when they run irregularly, broken and interrupted.

SEA-BOAT. A vessel that bears the sea firmly, without straining her masts, &c.

SEA-CLOTHS. Jackets, trowsers, &c.

SEA-MARK. A point or object on shore conspicuously seen at sea.

SEA-ROOM. A sufficient distance from the coast or any dangerous rocks, &c. so that a ship may drive or send, without danger of shipwreck.

SENDING. The act of pitching precipitately into the hollow between two waves.

SETTING. The act of observing the situation of any distant object by the compass.

To SET SAIL. To unfurl and expand the sails to the wind, in order to give motion to the ship.

To SET UP. To increase the tension of the shrouds, backstays, &c. by tackles, laniards, &c.

To SETTLE THE LAND. To lower in appearance. It is synonymous with TO LAY THE LAND.

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To SHAPE A COURSE. To direct or appoint the track of a ship, in order to prosecute a voyage.

SHEERING. The act of deviating from the line of the course, either to the right or left.

To SHEER OFF. To remove to a greater distance.

To SHEET-HOME. To haul the sheets of a sail home to the block on the yard-arm.

To SHIFT THE HELM. To alter its position from right to left, or from left to right.

To SHIP, To take any person, goods, or thing on-board. It also implies to fix any thing
in its proper place; as, to SHIP THE OARS, to fix them in their rowlocks.

SHIVERING. The state of a sail, when fluttering in the wind.

SHOAL. Shallow.

To SHOE THE ANCHOR. To cover the flukes with a piece of plank, to give it firmer hold in soft ground.

To SHOOT A-HEAD. To advance forward.

SHORE. A general name for the sea coast of any country.

To SHORTEN SAIL. Used in opposition to MAKE SAIL.

SLACK-WATER. The interval between the flux and reflux of the tide, when no motion is perceptible in the water.

SLATCH is applied to the period of a transitory breeze.

To SLIP THE CABLE. To let it run quite out, when there is not time to weigh the anchor.

To SLUE. To turn any cylindrical piece of timber about its axis, without removing it. Thus, to SLUE A MAST or BOOM is to turn it in its cap or boom-iron.

SOUNDING. Trying the depth of the water with a plummet, sunk from a ship to the bottom.

To SPELL THE MIZEN. To let go the sheet, and peek it up.

To SPILL. To discharge the wind out of the cavity or belly of a sail, when it is drawn up in the brails, in order to furl or reef it.

SPLIT. The state of a sail rent by the violence of the wind.

SPOON-DRIFT. A sort of showery sprinkling of the sea-water, swept from the surface of the waves in a tempest, and flying like a vapour before the wind.

SPRAY. The sprinkling of the sea, driven occasionally from the top of a wave, and not continual as SPOON-DRIFT.

To SPRING A MAST, YARD, &c. To crack a mast, yard, &c. by means of straining in blowing weather, so that it is rendered unsafe for use.

To SPRING A LEAK. When a leak first commences, a ship is said to SPRING A LEAK.

To SPRING THE LUFF. A ship is said to SPRING HER LUFF, when she yields to the effort of the helm, by sailing nearer to the wind than before.

SQUALL. A sudden violent blast of wind.

SQUARE. This term is applied to yards that are very long; as TAUNT is to high masts.

To SQUARE THE YARDS. To brace the yards, so as to hang at right angles with the keel.

To STAND ON. To continue advancing.

To STAND IN. To advance towards the shore.

To STAND OFF. To recede from the shore.

STARBOARD. The right-hand side of the ship, when looking forward.

STARBOARD-TACK. A ship is said to be on the STARBOARD-TACK, when sailing with the wind blowing upon her starboard-side.

STARBOARD THE HELM! An order to push the helm to the starboard-side.

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To STAY A SHIP. To arrange the sails, and move the rudder, so as to bring the ship's head to the direction of the wind, in order to get her on the other tack.

STEADY! The order to the helmsman, to keep the ship in the direction she is going at that instant.

STEERING. The art of directing the ship's way by the movement of the helm.

STEERAGE-WAY. Such degree of progressive motion of a ship, as will give effect to the motions of the helm.

To STEM THE TIDE. When a ship is sailing again the tide at such a rate as enables her to overcome its power, she is laid to STEM THE TIDE.

STERNFAST. A rope confining a ship by her stem to any other ship or wharf.

STERNMOST. The furthest a-stern, opposed to HEADMOST.

STERNWAY. The motion by which a ship falls back with her stern foremost.

STIFF. The condition of a ship when she will carry a great quantity of sail without hazard of oversetting.

To STOW. To arrange and dispose a ship's cargo.

To STREAM THE BUOY. To let it fall from the ship's side into the water.

To STRIKE. To lower or let down any thing. Used emphatically to denote the lowering of colours in token of surrender to a victorious enemy.

To STRIKE SOUNDING. To touch ground, when endeavouring to find the depth of water.

SURF. The swell of the sea that breaks upon shore or on any rock.

To SURGE THE CAPSTERN. To slacken the rope heaved round upon it.

SWELL. The fluctuating motion of the sea either during or after a storm.

SWEEPING. The act of dragging the bight or loose part of a rope along the surface of the ground, in a harbour or road, in order to drag up something lost.

SWINGING. The act of a ship's turning round her anchor at the change of wind or tide.

To TACK. To turn a ship about from one tack to the other.

TAKING-IN. The act of furling the sails. Used in opposition to SETTING.

TAKEN A-BACK. See A-BACK.

TAUGHT. Improperly though very generally used for TIGHT.

TAUNT. High or tall. Particularly applied to mast of extraordinary length.

TENDING. The turning or swinging of a ship round her anchor in a tide-way, at the beginning of ebb and flood.

THWART. See A-THWART.

THWART SHIPS. See A-THWART-SHIPS.

THUS! An order to the helmsman to keep the ship in her present situation, when sailing with a scant wind.

TIDE-WAY. That part of river in which the tide ebbs and flows strongly.

TIER. One range of any thing placed horizontally.

TOPPING. Pulling one of the ends of a yard higher than the other.

To TOW. To draw a ship in the water, by a rope fixed to a boat or other ship, which is rowing or sailing on.

TRIM. The state or disposition by which a ship is best calculated for the purposes of navigation.

To TRIM THE HOLD. To arrange the cargo regularly.

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To TRIM THE SAILS. To dispose the sails in the best arrangement for the course which a ship is steering.

To TRIP THE ANCHOR. To loosen the anchor from the ground, either by design or accident.

TROUGH OF THE SEA. The hollow between two waves.

TRYING. The situation in which a ship, in a tempest, lies-to in the trough or hollow of the sea, particularly when the wind blows contrary to her course.

TURNING TO WINDWARD. That operation in sailing, whereby a ship endeavours to advance against the wind.

VAN. The foremost division of a fleet in one line. It is likewise applied to the foremost ship of a division.

To VEER. To change a ship's course, from one tack to the other, by turning her stern to windward. The wind is said to veer when it changes more aft.

To VEER AND HAUL. To pull a rope tight, by alternately drawing it in and slackening it.

To UNBALLAST. To discharge the ballast out of a ship.

To UNBEND. To take the sails off from their yards and stays. To cast loose the anchor from the cable. To untye two ropes.

To UNBIT. To remove the turns of a cable from off the bits.

UNDER FOOT. Is expressed of an anchor that is directly under the ship.

UNDER SAIL. When a ship is loosened from moorings, and is under the government of her sails and rudder.

UNDER-WAY. The same as UNDER-SAIL.

UNDER THE LEE OF THE SHORE is to be close under the shore which lies to windward of the ship.

To UNMOOR. To reduce a ship to the state of riding at single anchor, after she has been moored.

To UNREEVE. To draw a rope from out of a block, thimble, &c.

To UNRIG. To deprive a ship of her rigging.

WAKE. The print or track impressed upon the surface of the water by a ship in her course, A ship is said to be In THE WAKE of another, when she follows her in the same track, or on a line supposed to be formed on a continuation of her keel.

To WARE. See TO VEER.

WARP. A small rope employed occasionally to remove a ship from one place to another.

To WARP. To remove a ship by means of a warp.

WATER-BORNE. The state of a ship, when there is barely a sufficient depth of water to float her off from the ground.

WATER-LOGGED. The state of a ship, become heavy and inactive on the sea, from the great quantity of water leaked into her.

WATER-TIGHT. The state of a ship, when not leaky.

WEATHER. Synonymous with WINDWARD.

WEATHER-BEATEN. Shattered by a storm.

WEATHER-BIT. A turn of the cable about the end of the windlass.

WEATHER-GAGE. When a ship or fleet is to windward of another she is said to have the WEATHER-GAGE Of her.

WEATHER-QUARTER. That quarter of the ship which is on the windward side.

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WEATHER-SIDE. The side upon which the wind blows.

To WEIGH ANCHOR. To heave up an anchor from the bottom.

To WIND A SHIP. To change her position, bringing her head where her stern was.

WIND-ROAD. When a ship is at anchor, and the wind, being against the tide, is so strong
as to overcome its power and keep the ship to leeward of her anchor, he is said to be WIND-ROAD.

WIND's-EYE. The point from which the wind blows.

To WINDWARD. Towards that part of the horizon from which the wind blows.

WINDWARD-TIDE. A tide that sets to windward.

To WORK A SHIP. To direct the movements of a ship, by adapting the sails and managing the rudder according to the course the ship has to make.

To WORK TO WINDWARD. To make a progress against the direction of the wind.

YAWING. The motion of a ship, when she deviates from her course to the right or left.

THE theory of working ships is nothing but the demonstration, supported with proofs, of the effects of every sail, and of the rudder, separately or all together considered, both with respect to the points where these machines are placed in the ship, and with respect to the different dispositions which either are given them in the changes of evolutions, or which arise from their various obliquities, when they present, more or less obliquely, their surfaces to the course of the water or the wind.

LEMMA.

I. IF A BODY STRIKES A SURFACE, IT COMMUNICATES TO IT ALL ITS PERPENDICULAR MOTION.

DEMONSTRATION.

If the body c, (fig. 1.) meets the surface A B, with a motion perpendicular to its middle, or center of gravity D, it will do it with the strength of all its perpendicular motion, which is the produce of its weight by its velocity; and will force it in the direction D G, perpendicular to A B. If the same body meets the same surface obliquely, and with the same velocity, it will impel it in the direction D G, with the velocity only of D E, which is equal to the angle of incidence H F. For, H F expresses the perpendicular velocity of the body H, towards the surface: and this is evident, if we consider that the movement H D, is composed of the two movements H F, and H E; and that there is no other movement, but H F only, which can meet the surface A B, since the other H E, is parallel to it.

But the part H F, of the motion of the body H, is perpendicular to the surface A B: whence it follows, that the body H impels, in the like perpendicular manner, that surface in the direction D G, with a force equal to the product of its weight by the velocity H F.

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CHAPTER I.

OF THE ACTION WHICH WATER OR WIND HAVE, BY THEIR PRESSURE, ON SURFACES.

2. FLUIDS are formed of an infinite number of particles, the minuteness of which is the cause why they communicate, by their shock, but very imperceptible degrees of motion, in the first instant of their action: and such is the weakness of their action, that it requires to be repeated a great many times before they can produce any sensible effect on the bodies they are to move.

It is easy to conceive, that the more specific gravity a body is possessed of, the stronger its impulse must be: therefore water, which weighs nearly eight hundred and fifty times more than air, ought to produce (the velocity being the same) an impulsion eight hundred and fifty times more than air would against a surface of the same size; moved in directions perfectly similar. And when it is known that the impulse of a fluid depends on its specific gravity, it will be easily understood that such an impulse must depend also on the extent of the surface which is struck. For, it is plain that the greater the surface is (the gravity, the velocity, and the direction of the fluid being the same), the stronger the impulse will be, admitting still the same proportion to be kept between the extent of that fluid's surface and that of any other surface put in comparison with it; because a surface of twelve feet square will always receive twelve times as much impulsion as would a surface of only one foot square. We must observe here, at the same time, that such parts of the fluid as strike, find more or less difficulty to recoil after the shock, according as the surface is more or less extensive; because, the greater the surface struck, the longer is the continuance of repulsion from their former directions impressed on the particles, which, by that very act of repulsion, receive a new direction, by which they are made to lose for a while the first movement they had during their primitive ones; whence it follows, that the shock of the subsequent particles must be altered; but this deviation, from the direct line, of the subsequent particles may be looked upon as almost nothing; since there is very little wanting, indeed, but all impulsions should be in the reciprocal proportions which exist between them and the surfaces on which they strike; allowing always all other circumstances to be alike.

3. It must be observed, that the rapidity of the fluid contributes doubly to the force of the impulse; for every particle strikes with so much the more strength as it acts with a greater velocity, and is at the same time followed by a greater number of new particles to shock the surface. So that the greater the celerity of the particles, the greater is the number of those which share the action, and the more powerful is the resistance they oppose to their being put out of their direct motion. But, if the fluid is possessed of five or six times more rapidity, it is evident that every particle enjoys like-wise five or six times more force to shock the surface which opposes the passage of them all together; as, on the side of the surface, there are five or six times as many particles to encounter in the same space of time: therefore such a surface, thus exposed to the shock of the fluid, will be struck with twenty-five or thirty-six times more force at one time than at another, since there are five or six times as many particles employed in the act of striking, and supported with five or six times as much

245

rapidity. Whence it may be concluded, that impulsions increase as the squares of velocities; or, rather that they are between themselves as the squares of their velocities, when all other circumstances are the same.

OBSERVATIONS.

When a surface is exposed to the course of a fluid, it is indifferent whether we consider that the fluid shocks the surface, or that the surface moves the fluid: or, again, whether we consider the fluid and the surface as having each their respective share of the velocity with which that surface receives the impulse of the fluid.

4. When the wind has little velocity, its action is observed to be but faint; but, when moving with rapidity, then it becomes capable of producing the greatest effects. This is easy to be conceived; for, if to the action of every particle of air, which is stronger by reason of its increased celerity, be added a greater number of particles striking at the same time, it is evident that its force will increase as the square of its velocity; which has already been demonstrated.

The same may be said of water, the impulse of which is almost like that of a solid when it acts, or is acted upon, with a great rapidity of motion. Whence we must conclude, that if that water meets perpendicularly a body which presents to it a great superficies, such a body must have the greatest solidity to be able to resist it.

5. Experience confirms this principle. For, a ship which drives to leeward does not divide the fluid with her side in a direct line; there is always some obliquity in the direction she pursues by her act of dividing. This obliquity proceeds from the little resistance she experiences from the fluid either at her stem or at her stern. So that, should she be driven ever so little to leeward, she glides always obliquely on the column of water which opposes her under her lee, in following a line more or less close to the direction of her length, than to the perpendicular which may be conceived to be draw, as lateral to her keel.

6. We have hitherto spoken of the impulse of fluids upon surfaces only, when considered as perpendicular: but, when that impulse becomes oblique, it is clear, that it must receive a great deal of diminution; since the motion of every particle will be discomposed on account of its acting only by its motion perpendicular to the surface, as has been demonstrated (fig. 1.), where the body H may be considered as a particle of a fluid, the impulse of which is proportionably less as the sine of the angle of incidence H D F, is diminished: therefore, in this case, when we consider the particle H, as a body, its impulse will be in the proportion of the different angles of incidence, which always express the respective velocities, these being considered in a direction perpendicular to the surface.

7. If, instead of one particle, we consider the whole surface as exposed to the course of all those which compose a fluid; it will appear evident, from what has been said, that the surface E F, (fig. 2.) which is oblique to the course of the fluid, presents to that fluid, a less surface than it would if it were perpendicular to it, like A B. So that each particle produces a less shock, and the particles which are at the same time contributing to the shock, are less in number. Now, as these two causes of diminution follow the same proportion, it results, that the impulsions of fluids are between themselves as the squares of the lines of incidence. Therefore, as soon as the impulse of a fluid, which strikes a surface perpendicularly, is known; that impulse, when it strikes the surface obliquely, is only to be diminished in the same proportion as the sine total I K, is to the square of the sine of incidence L K.

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The surface A B (fig. 2.) receives all the direct impulse of the fluid which strikes it perpendicularly, and which is contained between C D: but, the same surface, presented obliquely to the fluid in the direction E F, will receive but a part of the impulse, which will be proportional to the sine of incidence compared with the sine total I K, of the direct effort of every particle contained between the parallels E G, and F H, which inclose a much less space than the first, A C, and B D. Whence it is easy to conclude, that the diminution of the impulse of the fluid has diminished on two sides, and has consequently followed the proportion of the square of the sine total I K, to the square of the sine of incidence L K; for, there is a less number of particles employed in striking the surface, and with a smaller degree of velocity.

8. It follows, that we ought not to be surprised to see the velocity of a ship diminishing considerably when, after having run with the wind aft or large, the vessel is hauled closer to the wind. For, it is evident that all the sails which can possibly be spread in this last direction will receive but very little impulse, on account of their great obliquity to the wind, with which they cannot make an angle more open than 30 degrees, and sometimes much less, as will be demonstrated hereafter. So that the impulse has diminished, in proportion as the square of the sine total is to the sine of incidence of 30 degrees; that is is to say, as 4 to 1. Therefore, the sails, receiving but a very faint impulse, can communicate to the ship but a small motion; and that motion is full enfeebled by the resistance of the water on the lee-bow; which resistance increases, on one hand, by the inclination of the ship, and, on the other, by the greater surface which she presents to the water in the direction of her length; to which must be added, the decomposition of the absolute effort of the sails, the lateral part of which is now become much greater than the direct. Hence we find the rapidity of the ship's way is already diminished from three evident causes; to which another may still be added; and it is this: if the ship has an inclination to the horizon (as this always happens in oblique courses, and as we have already hinted,) and if the wind has ever so little force, there will result again, from that circumstance, a cause of diminution of impulse of the wind on the sails; because, in such a case, the sails follow that particular inclination of the ship called heeling: and this diminution of impulse will follow this particular proportion, viz. that in such a direction the square of the sine of incidence will be smaller than that of the sine total. Therefore, we see that the absolute sine of incidence diminishes in a twofold proportion, and receives that diminution from the compound ratio of the proportion which the sine total bears to the two sines of the obliquity of the yard with the wind, and of the inclination of the sail with the wind.

9. The impulse of the wind being continual, must necessarily communicate to the ship, degrees of velocity which, from instant to instant, are increasing, until there happens to be an equilibrium between the impulse of the wind on the sails and the resistance of the water on the bows, observing, that, in the courses where the ship sails with the wind abaft the beam, the first moment when the wind strikes the sails is the time when its impulse is greatest, and the resistance of the water the weakest; because, at that instant, the ship does not yet move in the fluid, not having yielded to the power of the wind: but, in a few moments, the velocity of the ship increasing, the resistance of the water on the bows increases also considerably: then the impulse of the wind on the sails is proportionably decreasing; because the ship receding, as it were, from the wind, must of course lessen its power on the sails. Thus the accelerating force is incessantly lessening from two causes; first, from the wind striking the sails with less force; and, second, from the greater part of its impulse being destroyed by the resistance of the water on the bows: a resistance which increases in proportion as the ship's way accelerates; for this opposition of the water is as a deduction from the effort of the wind;

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since, by its resistance, the water renders part of that effort ineffectual. Therefore, the rate of sailing will be the greatest possible when the impulse of the wind upon the sails shall be so diminished, and the resistance of the water on the bows so increased, as that the two forces acting in contrary directions are in a perfect equilibrium. Hence we must conclude, that the vessel will now enjoy a constant and uniform motion; for, the ship advances as if she were not subject to the action of any exterior force, the wind no longer having power to increase her velocity, because the resistance of the water on her bows prevents it; and, on the other hand, the impulse of the wind hinders the water, by its resistance, from retarding her course.

10. If a ship runs on a line perpendicular to the direction of the wind, the impulse on the sails is always the same, because she does not recede from the point from which the wind blows: but, when she sails close hauled, the impulse must be stronger; because she runs to windward, and draws nearer to that point. So that if the rate of the ship's sailing be great, the apparent angle of incidence diminishes in proportion to the two velocities, viz. that of the wind, and that of the ship.

The moment a surface which is suspended, or afloat, is struck by a fluid, that is the time of the greatest impulsion (if it were not in motion before,) and of the greatest resistance of the surface.

CHAPTER II.

OF THE CENTER OF GRAVITY.

II. EVERY solid has a center of gravity; that is to say, a point on which, it being suspended, it will have a perfect equilibrium; and on that point all the gravity of the body is united. Such, for example, is the rectangular parallelepipedon A B, (fig. 3.) the center of gravity of which is exactly in the middle of the solid, G; so that, if it be suspended from that point, as from G, to D, it will always be in equilibrium; because that solid being considered as regular, one of its halves must exactly balance the other; and were it not regular, the finding of this center would be much more complicated. Without engaging, therefore, in abstract difficulties, it will be sufficient, for our purpose, to make it appear that the center of gravity of a body heavier at one extremity than at the other, lies always in the heaviest part, with respect to the point which marks the middle of the length of the body. If to the solid A B, which is suspended in a perfect equilibrium by its center of gravity G, be added a weight E, in the center of the part A G, the equilibrium will then be lost, as it will increase the weight of this part, which will then overweigh the other half B G, by all the weight E, of which the part B G, becomes by so much lighter. To find, then, the centre of gravity, which is changed from G, to I, we must divide reciprocally to the weight of the two bodies, A G + E for the one, and B G, for the other, the interval F H; for it may be supposed that this half A G, of the parallelepipedon plus the weight E, is a body suspended by the center F, of the part A G; and that this point is the extremity of a lever H is, infinitely light, which bears also, at the other extremity H, taken for the center of the other part B G, all the weight of that part: so that,
if the body A G + E, weighs four times as much as the other weight B G, we have but to make the
interval F I, the fourth part of the other I H and the point I, will then be the center of gravity required of the solid A B + E, and the two bodies suspended by that point will be in perfect equilibrium;
for the weight A G E, + is four times as heavy as the other B G; but it acts with an arm of a lever

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F I which is only the fourth part of the other I H; therefore the two weights suspended by the point I, will preserve a perfect equilibrium, in whatever situation they may be placed, as they make, in fact, both but one, the heaviness of which may be supposed united in the single point I.

12 It follows, from what has been demonstrated, that a long lever is productive of a greater effect than a short one, when both are actuated by the same force; whence we must conclude, that the longest lever, or the greatest distance from the fulcrum or point of support, is proportional to the greatest weight.

It is very easy to be convinced of this truth, if we make one of the two following proportions: first, thus; the sum of the two weights AG + E + BG : FH :: B G : F I; or : : A G + E : I H.

We have supposed that the weight A G + E (fig. 3. ) weighs four times as much as the other B G, which I suppose to be two pounds; so that the sum total will be ten pounds. Then say: Ten, the sum of the two weights, is to the whole lever F H, as two pounds is to the less part, F I, of the lever divided into five equal parts: so that, if F I, is equal to two feet, I H, will be equal to eight feet, and F H, equal to ten feet. But we have also this proportion to make; viz. Ten pounds, the sum of the two weights, is to ten feet, the whole length of the lever, as eight pounds are to eight feet; but, admitting the distance F H, to be ten feet, the distance F I is found to be two feet, and that of H I eight feet; which demonstrates, that a power of two pounds on a lever of eight feet, is equal to a power of eight pounds on a lever of two feet; for the product of the extremes, in both the one and the other proportions, is equal to that of their means.

It ought also to be observed, that the center of gravity of a solid follows always the greatest weight with respect to the middle G, (fig. 3.) since the point I, four times as near the center F, of the heaviest body as it is to the center is, of the lightest body.

13. It follows, that the center of gravity A, of a ship (fig. 4.) is always before the point C which is the middle of her absolute length; for, the fore part B C having more capacity than the after part C D, must of course have also more weight: therefore, it carries the center of gravity C, forward, in proportion to its greater weight (which in large ships is from fifty to eighty tons,) and to the interval there is between every center of gravity of each particular part, both forward and aft.

14. When a ship is at sea, and loaded, the center of gravity may well be supposed not to change, unless the cargo be moved.

But it must be observed, that, as experience shows it, the fore or after part of the bottom of a ship plunges and labours more and more, in proportion as the wind acts with more or less force on the sails; because ships are generally not masted according to the point velique: * so that a ship which has the center of the effort of her sails ill-placed, draws always more water forward, or aft, when the impulse of the wind upon her sails is very powerful, than when she is at ease under her burthen.

* From the center of gravity of the floating line of a ship let a perpendicular be raised, and continued till intersected by the direction of the impulse of the water on the bows, in sailing directly before the wind; and where these two lines cut each other, there is the point velique, and where the center of effort of all the sails should be placed.

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THEOREM.

15. The center of rotation, or the point on which a body turns freely, is always on the other side of the center of gravity of that body, with respect to the point on which the moving force acts.

DEMONSTRATION.

IF the body B D, (fig. 5.) be struck in its center of gravity G, when it is perfectly at rest, it is evident (§ I.) that the two extremities, B and D, will advance equally on parallels: but, if it is struck in the point F, distant from the center of gravity, by any mobile such as A, when the body is subject to no friction, it will then have two motions with respect to its center of gravity G, on which are collected all the weight and the resistance. For, that center, not being held by any thing, is moved in the direction G g, parallel to the direction A I, of the effort of the mobile A, which strikes the body
B D, in the point F. So that the part B G, of that body receives the shock of the mobile A, which makes it pass from F to f, according to the direction of its motion A I. And as the other part, G D
of the same body shares that motion only in proportion as its parts are less distant from the point of percussion, F, (since the nearest parts of that point receive the greater share of the action,) in proportion as they remove from their first situation, they all describe, by the first effect of the shock, parallels B b, G g, and D d, to the direction A I, of the effort of the mobile A. These parallels are greater as they are more distant from the part shocked, and from its extremity B; because the resistance which the body B D makes against receiving the motion, cannot be in equilibrium with that which the power A, makes to lose part of its own motion, but as much as the two resistances are equal and directly contrary: therefore, the body B D, yielding to the impulse of the moible A, does not oppose to it a resistance, equal to its shock; it must then change its place and situation, in turning on the point R, marked by the meeting of two lines D R, and d R, drawn from the center of gravity of the body B D, in those two situations, before and after the shock; and as the circular motion of the body B D, is made always round the center of gravity, it is easy to conceive that the center, having taken the velocity G g, must continue to move equally in the same right line prolonged; and that the body having begun to turn, it must continue to do the same round its center of gravity, and at the same time, be carried in the direction A I, on the parallels B E, and D H as long as the force which puts it in motion exists. But, it must be remarked that, in proportion as it shall remove from its first situation B D, it will lose all the relations it had, in the principle of motion, with the point R; that is to say, that the point G, being transported to g, in the first instant of the shock, it will continue in the second and the following instants to be thus transported on the same line and in the same direction: therefore, the point of rotation R, will change in proportion as the body B D, removes from the second situation b d to take another E H; for the line H K,
will cut D R, in a point K, nearer the point from which the body was moved; and although the point of rotation R, be continually changing during the time of motion, it remains always on the other side of the center of gravity, with respect to the point of percussion, till at last the body B D, be so much turned, that the effort A I, may pass through the center of gravity G, in the direction D B; then the body D B, will cease to turn round a point situated on the part G D, prolonged, and will turn successively on different points of the part G B, which will then have passed to the opposite side.

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REMARKS.

16. IF the force of the mobile A, (fig. 5.) employed to turn the body B D, be greater or less, the velocity G g, of the center of gravity will be likewise increased or diminished in proportion as the mobile than act with more or less power. Consequently, when the body B D, changes its situation, the angle it will make with its first position will be proportional to the motion G g, or to the force employed in the shock, hence they are correspondent to one another. Therefore, all other circumstances being the same, the rapidity of the circular motion will be always in proportion to the force employed to produce it.

17. A method of increasing the rapidity of motion, and the angle of rotation, is to make the power A, (fig. 5.) act on a point more distant from the center of gravity G, than the given point F; for, it is clear, that if the distance G F be two or three times augmented, the other distance G R, from the center of gravity to the point of rotation, will become two or three times less; and the sides of the angle G R g, becoming consequently shorter, it follows, that the angle will be more open in the same proportion. Therefore, it is demonstrated that there are two sure methods of augmenting both the angle and motion of rotation of a body: the first consists of employing more force in the percussion, in order that the angle G R g should be as much increased as is the side G g, which subtends it.

The second is, to apply that force at a greater distance from the center of gravity of the body you wish to turn: for, in augmenting F G, G R is diminished; and the more the sides which form an angle are shortened (the side which subtends it still remaining the same), the more the angle is augmented. So that the angle of rotation is in a compound proportion both to the force employed, and to the distance of that force from the center of gravity: this angle is then, as the produce of that force multiplied by F G. Although the body be perfectly free, and take a direct motion G g, we must consider its center of gravity G, as the point of support, or F G as the arm of a lever; and the angle of rotation B R b is always proportional to the absolute force*, employed in the percussion.

18. Let us consider the body B D, (fig. 5.) exposed to the action of several forces at the same time, and it will appear that the angle of rotation will be proportional to the sum or difference of the absolute forces, according as they tend to turn the body B D, in the same or in contrary directions.

If the acting forces directly counteract each other, it is plain that their absolute effect, with respect to the center of gravity G, must be sought, and then deduct the excess of one from the other: then the angle of rotation will be proportional to that excess; instead of which, it will be proportional to the sum of the forces employed, if they act in concert, and in the same manner, to augment it. But if you take no notice of the angle of rotation, and wish to consider the center of gravity only as being transported from G to g, it is not necessary to find the sum of the absolute forces of the acting powers; but only to consider the forces in themselves, and then G g, will be found proportional to either their sum or their difference, according as they contribute to produce the same effects, or as they are opposite in their efforts. Suppose these forces equal between themselves, but acting in contrary directions on the extremities A and B, (fig. 6.) of the body A B, and on arms of equal levers. Then it is evident that the angle of rotation is double what it would be, if the body were struck by only one of these forces, and turned on its center of gravity: since the two parts, separated by the center, are struck

* By the term absolute force, we understand the force employed to turn the body, multiplied by the distance F G, from the center of gravity.

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equally, and at the same time, by forces which act perpendicularly in contrary directions. To prove this, observe that the equal powers, S and T, at the same time on the body A B, with equal levers, G K and G F: so that the extremity B passes to C. at the same time that A passes to D; and thereby the center of gravity, G, remains as if it were fixed in the same point which serves as a center of rotation; for, if one of the acting forces removes it from its first situation, the other, in opposing an equal force, will replace it.

If the power T exceeds the other S, it is evident that the center of gravity G, will be transported towards g, in proportion as the force T exceeds the other S; then the body A B could turn no longer on the center of gravity G, (§ Ts.); but on another point E, which would be on the other side of the center of gravity G, with respect to the point of percussion.

If the body A B, (fig. 6.) were struck at the two points, K and F, by two mobiles, S and I, exerting equal powers, with respect to the center of gravity G; it is plain that the whole body A B will be carried up on parallels, such as I T and S H, and that the sum of the two powers will act on the center of gravity G, since they are equal in every respect.

THEOREM.

19. A SAIL ACTS ALWAYS TWO WAYS ON A SHIP, WHEN IT IS NOT PERPENDICULAR TO HER
LENGTH.

DEMONSTRATION.

We have only to consider the sail A B, (fig. 7.) oblique to the ship and to the wind, and we must be convinced (§ 1, 7.) that it is impelled in the direction C D, with a force expressed by the square of the sine of incidence of the wind upon the sail. Therefore, what we are going to say here for the present case is to be understood as applicable in all others, in which the sail shall not be perpendicular to the length of the ship; for, then, she would go only in the direction of her length from C to E, or from C to F, according as the sail might be full or a-back.

If C D be equal to the impulse of the wind upon the sail, as expressed by the square of the sign of incidence A V we have only to form the right-angled parallelogram G H, to be convinced that such a direction is composed of the two effects C H and C G, which it produces with respect to the body E F, upon which it acts in impelling it in the direction C D.

REMARK.

The more the yard A B (fig. 7.) shall make the angle A C E acute, the more the effect C H will augment, and the other C G diminish; for, the more the angle A C E becomes acute, the more its equal D C H or C D G (§ 22) will be acute also; so that C D, which is perpendicular to the center of the yard, will approach more to C H, the other perpendicular to the length of the ship E F; which cannot happen without increasing the ship's tendency to fall off in the direction C H, and increasing likewise the cause C D, which follows in that increase the same proportion as the square of the sine of incidence augments (§ 1, 6, 7.). But this increase of the impulse C D is not sufficient to preserve the effect of the sail in the direction of the keel C G. On the contrary, it diminishes in the proportion of the decrease of the sine A C E or C D G; whence it follows, that you never can augment the impulse of the

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wind by shifting the situation of the sail, when it is properly trimmed, without lessening the rate of sailing (§ 28.), when neither the ship changes her course, nor the wind shifts.

20. It might, in the same manner, be demonstrated, that the more open the angle A C E of the sail A B is with the keel, the more its effect C G, in the direction of the ship's length, will increase in the same proportion as the increase of the sine of that angle, when the impulse of the wind upon the sail is the same; for, the sines of the angles are in proportion to their opposite sides in the triangle C D G, of which the angle C D G is equal to the angle A C E.

If the impulse augment also (§ 3.), the two effects, C G and C H it, will augment proportionally.

21. If the sail A B receive the impulse of the wind E on its forward surface, it would still act in two ways on the ship, by forcing her first a-stern in the direction C F, and then to leeward in the direction H C: to be convinced of this, reverse the parallelogram, by tracing it on the after part of the yard towards F, and use the same reasoning.

THEOREM.

22. THE ANGLE A C F (fig. 8.) FORMED BY THE YARD A B, AND THE KEEL F C OF THE SHIP, IS EQUAL TO THE ANGLE D C E COMPREHENDED BETWEEN THE PERPENDICULARS D C TO THE YARD AND E C TO THE KEEL, IN THE LIKE MANNER AS THE ANGLE C D G.

DEMONSTRATION.

The angle A C D is right, since C D is perpendicular on A B: the other angle F C E is right also; for C H is perpendicular on F I; therefore the arc A D is equal to the arc F H; and if, from these two equal arcs, be taken away the common one F D, the remainders A F and H D will be equal: because, when equals are taken from equals, the remainders must be equal.

Secondly, the angle C D G in the parallelogram G E is alternate to the angle D C E: therefore it is equal to it; therefore it is also equal to A C F.

23. It follows, that the angle B C H is equal to the other angle D C F; for, if from the two equal arcs A D and B D, be taken the other equal arcs F A and D H, the remainders F D and H B will be equal also.

REMARK.

24. The few principles of Geometry here given, and which will be found of great service in the sequel, ought not to discourage. We make use of them now, only to establish principles as simple as they are sure, and to leave nothing to doubt or conjecture in the following part of this theory, which is in itself very abstruse. We shall however be obliged to use again a few more demonstrations of this kind.

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CHAPTER III.

OF THE MOST ADVANTAGEOUS ANGLE OF THE SAILS WITH THE KEEL AND THE WIND, IN ORDER
TO DETAIN THE GREATEST RATE OF SAILING, ON An OBLIQUE COURSE.

25. IN most ships the sails make with the keel an angle A D R (fig. 9.) of 40 degrees, or thereabouts, (some more, some less,) when close-hauled. We are now to undertake to make it appear that this angle is not the most favourable to run with the greatest velocity, in getting to windward. It should be much more oblique; but as it is not possible, in practice, to attain the greatest perfection, we must be contented to approach it as near as possible, in great ships, by reducing the angle A D R to 30 degrees only. This will be so much the more easily done, as in every ship the two foremost shrouds of each lower mast can be suppressed. For it must be observed that in the movement of pitching and rolling, the masts always incline forward, in the direction D E of the effort of the sail; so that the shrouds which are abaft, and cat-harpened in, are sufficient to support the masts, since they act nearly opposite to the effort of the sail. Besides, should there be reason to expect bad weather, preventer shrouds may easily be fastened to the strops which are always ready hung for that purpose. This practice is so much the better grounded, as the number of those preventers can at any time be increased as circumstances or necessity require.*

Therefore, we shall, for the future, consider the angle A D R, which is the most oblique in practice, as fixed at 30 degrees, though, in some ships, it may happen to be more acute: a circumstance to which particular attention should be paid.

26. Among all the angles A D R, B D R, and H D R (fig. 9.) which the sail A Z, can make with the keel in the same course D R, it is evident there must be one more advantageous than the rest, to produce the greatest velocity possible in the most oblique course. That angle of the sail and the keel is not what we propose directly to determine, since it is impossible to render it more acute than 30 degrees, the term to which we have fixed it in practice: but it will serve us to determine the most favourable angle of incidence A D V of the wind upon the sail, and which is the most advantageous to run with the greatest rapidity on all oblique courses between close-hauled and wind abaft.

27. Before we enter upon the demonstration of the rule which must be followed in practice, the principle which serves to demonstrate its utility must be first established. It may be recollected that impulsions (§ 7.) are between themselves as the squares of the lines of incidence. Therefore, to judge if it is advantageous to render the angle of incidence A D S or A D V of the wind upon the sail A Z, more or less acute, we must examine if the square of the sine of incidence A F, or the total impulsion D E, increases more or less than the squares of the sines of incidence B C and H I, or than their correspondent impulsions D G and D K, proportionally to the diminution or increase of the sines of the angle of obliquity of the sail with the keel A T, B Y, and H L: for, if the square of the sign of incidence H I, or the impulsion D K, does not increase so much proportionally, as the sine of obliquity

* This recommendation of M. Bourde, to suppress the two foremost shrouds of each lower mast, in order to brace up sharper, we are warranted in saying, cannot be followed in the British navy. It was lately determined, upon a consultation of the Officers of the King's Yard, the question having been referred to them, that the present number and dimensions of the rigging of ships could not be advantageously altered, or safely diminished. And, as to occaisonally casting them off; it may be rendered, by the inevitable accidents of navigation, highly dangerous; as; for instance, in case of being suddenly taken a-back, this lessening of the support of the mast might be attended with its loss.

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A T diminishes in becoming equal to L H it is evident that the position of the sail A D is more favourable than when it is situated in the direction D H: and if the square of the sine of incidence B C, or its correspondent impulsion D G, diminishes more in proportion than the sine A T augments, in becoming equal to the other sine of obliquity B Y, in the other position of the sail; it is an evident proof that its situation A D is still more favourable than if it were in the position B D, and that there is even no better situation than A D, whether the angle of incidence A D V be increased or diminished.

28. To prove it, we shall consider (fig. 9.) the absolute impulsions D K, D E, and D G, as correspondent with the lines of incidence H I, A F, and B C, and proportional to the squares of these same lines; then, on these diagonal lines, if we draw the rectangles X N and M O, in order to dissolve those total impulsions D E and D G, it will appear evident that the direct effort D X in the direction of the keel, is the greatest possible, when the tangent A S of the angle of incidence is double the tangent A R of the angle of obliquity of the sail with the keel; for, if the angle of incidence be opened ten degrees, by placing the sail in the situation H D, it will appear that, though the total impulsion D K is augmented in the ratio of the square of the new sine of incidence H I to the first A F, the partial effort D M, in the direction of the keel, will be nearly by one tenth less, in this situation of the sail H D, than in the first A D. The direct impulsions D M, proceeding from the total ones D K and D G, are equal, because these last have augmented or diminished in the same ratio as the lines H L and B Y have lessened or increased in proportion to the square of the sine of incidence A F, and to the sine of obliquity A T. These direct partial impulsions D M and D X are in a compounded ratio of the sines of obliquity H L, A T, B Y, equal (§ 22.) to those of the angles D K M, D E X, D G M, and of the total impulsions D K, D E, and D G; for, if the total impulsion augment by a movement of the sail, the sine of obliquity diminishes: so that from the total impulsions can at any time be deduced the direct ones for every possible angle of incidence. We might very well verify by calculation this demonstration, which proves that the tangent A S of the angle of incidence must always be double the tangent A R of the angle formed between the sail and the keel, agreeably to the situation of the sail A Z; since if any other position be given to it with respect to the wind V, whether it be in the direction H D ten degrees more open than A Z, or like B D ten degrees more oblique, a result, as D M, in the direction of the keel, will ever be found less than D X.

OBSERVATIONS.

AS the vanes always indicate the apparent direction of the wind, on all the courses the ship can sail, the angle which the wind makes with the course, or the keel, cannot fail being easily known if there is no lee way; let that angle with the sails be parted into two others, so that the angle of obliquity of the sails with the course may have its tangent equal to half the tangent of the apparent angle of incidence of the wind upon the sails. On this foundation, it will be ease to form a table which will always show both the apparent angle of incidence, and that of the obliquity of the sail with the keel, or with the course. This table will serve for all oblique courses, provided the after sails cover those forward only in a trifling degree; for, should they becalm them much, they must, for other considerations, be braced up a little more to the windward; but always leave the apparent angle of incidence of the wind upon the sail more open than that between the sail and the keel, or the course.

29. When it is desired to gain to windward as much as possible, without absolutely wishing to sail with the greatest velocity, let the direction of the coast under the lee be supposed to make with the absolute direction of the wind (which must as near as possible be known) an angle of 90 degrees; or, in the sea phrase, blowing dead on shore: let the angle A C E (fig. 10.) formed by the sail and the keel, be known to be 30 degrees, let the lee-way be also known to be ten degrees, the angle E C I between the sail and the course will consequently be 40 degrees, which you must take from the total angle V C L 90 degrees; then there will remain 50 degrees, the half of which, 25 degrees, is to be taken for the absolute angle of incidence V C E, and for its equal I C L; so that the ship A B will go 55 degrees from the wind when she is close hauled, and will consequently recede as much as possible from the point D on the coast, the direction of which makes an angle of 90 degrees with the absolute direction of the wind V K.

But, if the situation C L, (fig. II.) of the point D, from which you wish to move, made an obtuse angle V C L, with the positive direction of the wind V M; then, the tangent of the apparent angle of incidence V C E must be made double the angle of obliquity E C I which the sail makes with the course, at the same time that the angle I C L, of the course and the coast shall be made equal to the angle V C E, formed by the real direction of the wind V K, and of the sail: so that two considerations must at once be attended to. For example: the angle A C E, formed by the sail and the keel, is 30 degrees; then, according to the first principle, it will be necessary that the apparent angle of incidence V C E, would be 49° 6'; and, if the difference between the apparent and real direction of the wind be 10 °, there will be 59° 6' for the angle which
the sail E V, makes with the real direction of the wind V M: so that the angle L C I, of the course and the object stood from, must be found also to be 59° 6', and the total angle L C V, will then be 148° 12', adhering to the two principles of sailing with the greatest velocity, and of getting to windward of the point D, as much as possible, at the same time; while the angle L C V, formed by the apparent direction of the wind and that of the coast from which the ship moves, will be only 138° 12'. The yawing and the different velocities of the ship render the angle formed by the two directions of the wind, (the real and the apparent,) more or less open. If the ship has more velocity at the same time, or if the course approaches more to the direction of the wind, it will appear by the vanes that the wind draws forward, and the angle of the two directions of the wind will augment. If the ship falls off, and yet still preserves the same velocity, or if her velocity decreases without altering her course, the wind will seem by the vanes to draw aft, and the angle of the two directions will diminish; so that, whenever the ship shall have velocity or run obliquely to the wind, there will always be a difference between its real and its apparent direction. In short, if the ship run exactly before the wind, or have no motion at all, there will be then no other but the real direction of the wind shown by the vanes: but happen how it will, in oblique courses this is however certain, that the sails are always struck by the absolute direction of the wind; because, their position being once fixed by the braces and bowlines, it can no more change, but continues as steady as the real direction of the wind; for it is the vanes only which, being moveable, fix themselves in a middle direction between the absolute tendency of the wind and the course of the ship; whence we may easily conclude, as we did before, that the apparent direction of the wind shown by the vanes, is

256

a medium between the respective velocities of the ship and of the wind; since that direction necessarily partakes more of the greater velocity than of the less: so that, if the ship runs East, with the wind at South, having the fourth part of the velocity of the wind, the vanes will show S. S. E. 4° 30' s for the apparent direction of the wind.

ARTICLE II.

THEOREM OF M. BOUGUER.

The velocity and real direction of the wind is C M(fig. II.) suppose the ship A B, of which E F is the sail situated at pleasure, to draw the course C I while the particles of air run in the direction C M: if, from the point I, be drawn I K, parallel to the sail E F, till it cuts the direction of the wind, V K, in the point K, there will be given the three points C, I, K, through which draw the circumference of a circle C I L K, and that circumference will show the extent of the forces acting on the ship, at the same time, in following the course C I, provided her sail be always trimmed in the same manner with respect to her keel.

DEMONSTRATION.

The apparent or relative velocity of the wind is represented by I M (fig. II.) in the course C I; and as I K is parallel to the sail E F, the angle M I K is equal to the apparent angle of incidence V C E. But to be more explicit: the wind strikes the sail with its apparent or relative velocity I M, (and not with its absolute velocity, because of the motion of the ship,) and with an angle of incidence M I K=V C E: so that, if the ship runs close hauled or perpendicular to the direct wind V C, I M will become in both cases stronger than the absolute velocity; because the ship will either approach to the source of the wind, or not recede from it. But the impulse on the sail is proportional to the square of the velocity I M, multiplied by the square of the sine of the angle of incidence M I K, equal to the angle V C E (§ 3. & 7.) and the proportion M K: sine K I M : : sine M K I which furnishes us the triangle K I M, shows us that M K x sine M K I=M I x sine K I M; squaring the
two products, and substituting the sine of the angle V K I in the room of the sine of the angle M K I which is equal to it, since they are the supplement of each other, we shall then have this other
equation: (sine V K I)2 x (M KO)2 = (sine K I M)2 x (M I)2; whence it follows, that instead of expressing the actual impulse of the wind upon the sail by the square of I M, multiplied by the square of the sine of the angle K I M, it may be expressed by the square of M K, multiplied by the square of the sine of the angle V K I, or of its equal V C E, formed by the absolute direction of the wind V M, and the sail E F.

We must not forget to be very attentive to this; viz. that the impulse of the wind upon the sails is in equilibrium with the effort of the water on the bows, or that they are exactly equal and contrary when the ship is come to an uniformity of motion (§ 9.) as here we suppose her to be. Besides, the impulse of the water on the bows is proportional or equal to the square of the velocity of sailing C I, (§ 3.) so that the square of the velocity of sailing C I, is equal to the actual impulsion of the wind
upon the sail expressed by the square of K M, multiplied by the square of the sine of the angle V C E; and if s be supposed equal to the sine of V C R, or of V K I, we then always find (C I)2=(S)2 x (K M)2. The

257

The first term in this equation represents the impulse of the water on the bows, and the second expresses the effort of the wind upon the sails; and, if the square roots of the one and of the other be taken, it will be found C I = S x K M; that is to say, that the very velocity of sailing C I, will be continually equal or proportional to the product of K M by the sine S of the angle V C E or C K I. The proportion between these quantities depends on the density of the two fluids, and on the magnitude of the surfaces struck: but it will be the same in all the different courses.

The different velocities of sailing C I, have a constant and given proportion with the products
S x C K and C I x sine C I K; for the triangle C I K gives S : C I:: sine C I K : C K, which forms this
equation, S x C K = sine C I K x C I; and all the angles C, I, K, are constant and known, since they are equal, being alternate to that which the sail makes with the course. But, as the velocity C I bears a continual and constant proportion with the product S x K M, and as it bears also a constant proportion with S x C K, it follows that S x K M : S x C K :: K M : K C; so that the point K always divides C M in the same proportion: the point K is then invariable when the sail, as well as the lee way, are both the same; (which never happens, however, as will be made appear (§ 47.) hereafter) but, in admitting those two hypotheses, which never can deviate from the truth but in respect to the lee way, which is always variable in the same ship, according to the different circumstances of wind, sea, velocity, sail, and course, it ought then to be concluded that all the points, 1, &c. will be situated on the circumference of a circle; for, without that, the angles C I K equal to those which are formed by the course and the sail, and which are supported on the same chord C K, would not be equal.

COROLLARY.

Admitting therefore, (fig. II.) that the velocities are continually proportional to the sines (whatever they be) of the angles V C E, which the sail makes with the absolute direction of the wind, provided the sail be always trimmed in the same manner with respect to the keel, and that, in the triangle C I K, the side C K and the angle C I K are constant, and the velocities of sailing C I are proportional to the sine of the angle C K I equal to the angle of incidence V C E; it follows, that, all the other conditions being the same, the more the sine of the angle V C E is augmented, the greater will the rate of sailing be; so that, if you want to carry it to the greatest rapidity, you have only to make a right angle of the angle V C E formed by the absolute or real direction of the wind with the sail; then the velocity C I will no longer be a simple chord in the circle C K I, but a diameter. This holds good for all the ships which have but one sail set; but, whenever they shall have several, the greatest velocity will be when the apparent angle of incidence of the wind upon the sail makes a right angle with the course; because then the sails will easily make with the apparent wind, an angle, of which the tangent will be double that of the angle they make with the course, without their becalming one another; while, at the same time, the ship will receive all the absolute impulse of the wind, because she does not recede from it, and it is the time when the greatest surface of sail is exposed to its impulse. The same advantage of the greatest velocity will still be had, when the apparent direction of the wind makes an angle of an hundred degrees with the course; and in this situation, the velocity will in some degree be increased. In a word, whenever the after sails do not becalm those forward, the ship's rapidity may always be increased, by trimming the sails as directed (n. 28.) but when the sails take the wind from one another, an increase of velocity can no longer be pretended to.

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We are now going to demonstrate the exactness of the rule given before. (§ 29.) When it is required to get off shore, or recede from a given right line with all possible expedition, or to keep absolutely as close to the wind as the ship will lie; C M (fig. II.) is the absolute direction of the wind; the circle C K L I marks all the points at which the ship can arrive with the same sail, the same disposition, without alteration of lee-way, and at the same time; and C L is the right line from which she is to move. Knowing the angle that line makes with the absolute direction of the wind V M, it is evident that the point I of the circumference, where the course ought to end, is in the middle of the arc C I L, of which C L is the chord: and all the points from one part to the other of C I, where the ship can come to at the same time, are less distant from C L, since D I, perpendicular to C L, divides it into two equal parts, and is the longest of all the perpendiculars which can be drawn from the circumference C I L; but the point I, cannot be taken without rendering the angle L C I equal to the angle C K I, which itself is equal to the angle V C E.

ARTICLE III.

A TABLE OF THE SITUATION OF THE SAILS TO RUN WITH THE GREATEST VELOCITY.

M. BOUGUER.

Angles of theapparent directionof the wind andcourse

Angles of the sailswith the keel.

Angles of Apparentincidence of thewind on the sails

D.

M.

D.

M.

D.

M.

180,

00

90,

00

90,

00

176,

15

87,

30

88,

45

174,

37

86,

25

88,

12

172,

30

85,

00

87,

30

168,

44

8z,

30

86,

14

164,

58

80,

00

84,

58

161,

10

77,

30

83,

40

157,

22

75,

00

82,

20

153,

33

72,

30

81,

03

149,

41

70,

00

79,

41

145,

48

67,

30

78,

18

141,

53

65,

00

76,

53

137,

55

62,

30

75,

25

133,

54

60,

00

73,

54

129,

50

57,

30

72,

20

125,

42

55,

00

70,

42

121,

31

52,

30

66,

01

117,

14

50,

00

67,

14

112,

53

47,

30

65,

23

108,

26

45,

00

63,

26

a ..

..

..

..

..

.. b

103,

53

42,

30

61,

23

99,

13

40,

00

59,

13

94,

25

37,

30

56,

55

89,

28

35,

00

54.

28

84,

23

32,

30

51,

53

79,

05

30,

00

49,

06

73,

39

27,

30

46,

09

68,

00

25,

00

43,

00

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N. B. The foregoing TABLE can be of no great service, except in the eight last circumstances under the line a, b; because, in all the cases mentioned above that line, the sails will cover one another too much.

OBSERVATIONS.

When a fast sailing ship (such as will, on a direct course, or right before it, take a third or a fourth part of the velocity of the wind) comes to run with the same quantity, or more sail, on a perpendicular to the apparent direction of the wind, then she acquires a greater rapidity of sailing with respect to the velocity of the wind; the angle made by the two directions, the apparent and the absolute, is at that time very considerable; it may be from 18° to 22° 30'; and if the ship hauls quite close by the wind, the angle will still be nearly the same; for, her velocity diminishes: but, as it is in sailing by the wind that it is most essential to know the greatness of the angle between the two directions of the wind, let the angle between the directions of the ship's head on the different tacks be observed, without paying any regard to the lee-way, but just to the exact point on which the ship stands, before and after going about, when strictly by the wind, neither too much to leeward nor to windward; and when you have determined that angle, from two or three observations, halve it, and then you will have the angle formed by the keel and the absolute direction of the wind; by which you will know the quantity she will come to upon the different tacks, and will never be deceived with respect to the lying on astern having gone about: a mistake pretty commonly made by those who pay attention only to the apparent direction of the wind, which always makes with the real one an angle more or less open in a compound ratio of the greatest velocity with the greatest obliquity of the course of the ship, with respect to the direction and the absolute velocity of the wind; things which vary in all ships, because they have not all the same advantage of sailing with the same rapidity in similar circumstances.

CHAPTER IV.

OF THE SAILS WHICH ARE BEFORE THE CENTER OF GRAVITY OF A SHIP.

30. THE sails which are before the center of gravity of a ship, are the sprit-sail, sprit-sail top-the jib, the fore-top-mast stay-sail, and the fore stay-sail.

Besides these sails there are, on the foremast, the foresail, fore-topsail, fore-topgallant-sail, and fore-topgallant-royal-sail, with their respective studdingsails. Now these four last sails may be regarded as only one large sail, wide at the foot and tapering towards the head, and which can be reduced, as occasion requires, either by taking in the royal, or by reefing the fore-top-sail, or even taking it quite in, if necessary, to have the fore-sail only set; or by hauling the fore-sail up, if nothing but the top-sail is wanted. It must notwithstanding be observed also, that the different parts of the whole sail may, in certain cases, be worked differently the one from the other; as, for example, in reeving the top-sail, or in taking in either the one or the other. But, when you want to set them to work all together, either for making a course, or performing some evolution, they must all be braced and trimmed in the same form, and with the greatest uniformity possible. Therefore, whatever we shall say concerning one of them in any operation, is to be understood to be the same with respect to all the rest.

The main-stay-sail, the main-top-mast stay-sail, the middle-stay-sail, and the main-top-gallant stay-sail, are likewise sails of the fore-part of the ship's center of gravity.

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ARTICLE I.

OF THE EFFECT OF THE FORE-AND-AFT-SAILS, WHICH ARE ON THE FORE PART OF THE CENTER
OF GRAVITY OF A SHIP.

31. THE jib and stay-sails being of a triangular figure, their center of gravity is easily found; and that point is to be considered as the part, in all these sails, on which the whole effort of the wind is united, when they are exposed to its impulse, in whatever way it strikes them.

The particular effort of each fore-and-aft sail being on the fore part of the center of gravity of the ship, it follows that the total effort of all these sails must be there too; and that, if the ship was in a perfect equilibrium with respect to the wind, before her sails were set, she will lose it immediately after (§ II.) they will make the fore part of the ship obey the wind, whenever it strikes them perpendicularly or obliquely. For, it must be observed, that almost all these sails have their tacks; in the middle of the ship, and their sheets lead to the sides; so that they make with the keel a very acute angle: whence it is easy to conceive, that the perpendicular which would be raised on the exterior surface of these sails, in the direction of their effort to leeward, from their center of gravity, would differ but very little in the lateral direction from a perpendicular to the keel. From this we may therefore conclude, that these sails would have but very little effect to accelerate the rapidity of sailing with respect to their position, if it was not demonstrated that they are very advantageous in going by the wind. They make the ship steer well, and are particularly useful when a ship gripes much: and, when they do not take the wind out of any of the lower sails, they ought to be used, particularly when one is obliged to sail by the wind, or to run not very large. The jib and fore-top-mast staysail must be preferred, because they are at all times useful when they can receive the wind; for, by their position, they can take the wind out of any of the other sails, and their particular effect in veering is considerable, not only on account of their great surface, but because they act before the point, on which the ship turns, with a very long arm of a lever (§ 17.) On the other hand, all the sails draw the ship a-head in raising her: for the direction of their effort ascends obliquely towards the horizon; therefore, they do not make her plunge in the water, which is an advantage peculiar to them. Experience has confirmed their utility on all occasions when they can be employed without taking the wind out of the other sails.

ARTICLE II.

OF THE EFFECT OF THE FORE-SAIL, FORE TOPSAIL, FORE TOP-GALLANT-SAIL, AND SPRIT-SAIL,
IN THEIR DIFFERENT SITUATIONS.

32. WHEN the sail A B (fig. 12.) is trimmed close to the wind which blows from the point V, it is impelled in the direction C D (§ 7.) with a force expressed by the square of the sign of incidence, and composed of the two effects C E and E D (§ 19.) But, as the center of effort of that sail A B is on
the fore part of the center of gravity of the ship H, and as its power C D is always decomposed between those two effects C E and E D, it follows, that the effect of this sail is to cause the ship to bear away; while it keeps up at the same time, and even augments, the rapidity of sailing.

261

33. If the fore-sail A B received the impulse of the wind perpendicularly, it would still produce the effects of bearing away, and augmenting the rate of sailing, for the reasons just given above, but more effectually would it do so (§29.) on account of the increase of the impulse of the wind upon the sail.

34. IT follows, from what has been said, that when the sails upon the fore-mast are full, on the same side they are tacked, being braced obliquely to the keel, there is always one part of their effort, in proportion to their obliquity, which acts to make the ship bear away; while the other part of their effort acts at the same time to accelerate or keep up the rate of her sailing.

35. When the sails A B of the fore-mast (fig. 13.) are situated obliquely with respect to the keel, and receive the wind in them, on the side of the sheet B, they act upon the ship in bringing her up to the wind, because their effort D G being discomposed, as customary, the lateral part D F carries the fore part of the ship towards the source of the wind V, in carrying her from D to F.

REMARKS.

36. IN general, when the yards are square or perpendicular to the keel, it is evident that they will act on the ship, only by impelling her right in the direction of the keel, from stern to head, or from head to stern, with more or less velocity, in proportion to the impulse of the fluid which strikes them.

37. When the sails A B on the fore-mast (fig. 14.) receive the impulse of the wind V, on their surfaces forward, they will make the ship both go a-stern and sail off; because the direction C E of their effort, being turned towards the after-part, serves as a diagonal to the parallelogram F D, which, by discomposing it, will show us those two effects C F and C D, the first of which takes its direction with that of the keel from forward aft; while the second takes it in a lateral direction in making the ship to turn.

38. When the wind blows between the keel and the yard, the ship comes to, until the point G (fig. 14.) is in the direction of the wind V. But, as soon as this is done, it is evident that she falls off; for the point G recedes farther and farther from the direction of the wind. Whence we may remark, that, as soon as the weather part of the sail catches a-back, on the tack side, the angle of incidence of the wind on it goes continually increasing, till the ship has fallen off so much, that her sail becomes perpendicular to its direction: and, if the vessel continues to fall off, then the angle of incidence diminishes more and more, till the sail is parallel to the course of the wind which comes from the tack B, or, as it is called, shivering.

262

CHAPTER V.

OF THE SAILS WHICH ARE ABAFT THE CENTER OF GRAVITY OF A SHIP.

39. THE main-sail, main-top-sail, main-top-gallant-sail, and main-top-gallant-royal-sail, and their respective studding-sails; the mizen-stay-sail, mizen-top-mast-stay-sail the mizen-course, mizen-top-sail, mizen-top-gallant-sail, and mizen-top-gallant-royal-sail; are all sails, which are placed abaft the center of gravity of a ship, which is also abaft the point round which the total effort of the sails is placed.

ARTICLE. I.

OF THE EFFECT OF THE FORE-AND-AFT SAILS ABAFT THE CENTER OF GRAVITY OF A SHIP.

40. THE center of effort of these sails being abaft the center of gravity of the ship, it follows that they always force the after-part of the ship to leeward, and consequently contribute to bring her to the wind, as soon as they receive its impulse; for, that movement of the after-part of the ship cannot happen, without the head approaching to the direction of the wind.

The fore-and-aft sails being in general situated very obliquely, it follows, consistently with principles, that they are very advantageous for sailing by the wind. Therefore, we must not neglect augmenting them: observing, at the same time, that they do not take the wind out of one another, nor becalm the principal sails. They are only to fill up the space between the masts fore and aft, in sailing near the wind, in order that no wind may be lost.

ARTICLE II.

OF THE EFFECT OF THE SQUARE SAILS OF THE MAIN-MAST, AND OF THE MIZEN-TOP-SAIL, THEIR DIFFERENT OBLIQUITIES.

41. AS we have already demonstrated (§ 19.) that when the sail A B (fig. 15.) is trimmed obliquely to the keel, it produces evidently two effects on the ship; it must therefore follow, that, in dissolving its power C D, we shall find its compound effects, the one C F, in the direction of the keel which produces the velocity, and the other C E lateral, which (in forcing the after-part of the ship to leeward, by its action on the point C abaft the center of gravity G of the ship) occasions her to come to the wind; for that motion of the stern from C to E cannot take place, unless the fore-part acts contrarily in coming towards the point from which the wind blows, V.

42. If the sails A B were more or less oblique to the keel, they would still have the same effects of keeping up the ship's velocity, and bringing her to the wind. And, if they received its impulse perpendicularly, it would still be the same thing, producing those two effects, however, with greater efficacy than in any other situation with respect to the wind, because then they receive its greatest possible impulse for the time.

263

43. When the sails A B (fig. 16.) of which the center of effort C is abaft the center of gravity of the ship, receive the impulse of the wind V on the sheet side, being placed obliquely to the keel, they will cause the ship to fall off, by forcing the after-part from C to I, towards V, the source of the wind, while they will, at the same time, keep up the velocity C I. For, this motion of the after-part E towards V, cannot be executed without the fore-part E going, as it moves off, in a contrary direction; and she will continue to fall off till the keel E H be right in the direction of the wind V C, or right aft; then the ship will come to the wind, as shown in the two preceding articles.

It may be remarked that, in this movement of the, ship the angle of incidence goes continually increasing till the wind is perpendicular to the sails.

44. When the sails A B (fig. 17.) of which the center of effort is abaft the center of gravity G, shall receive the impulse of the wind V on their forward surfaces, they will make the ship come to the wind, and go a a-stern at the same time. For the direction of their effort C D may be dissolved between the two efforts C F, in the direction of the keel, from forward to aft, and C E lateral and perpendicular to the keel; so that the after-part C H is forced to leeward from C to E, while the fore-part I approaches, by a contrary motion, the point of the wind V. In this case, therefore, the ship comes to, and goes a-stern.

45. When the ship is so far come to the wind, that the fore-part I (fig. 17.) has come into its direction, it is evident, that she will fall off more and more; for, that point I will constantly move from the point of the wind V; therefore, it is demonstrated that, in this case, the sine of incidence is continually decreasing more and more, till it is reduced to nothing. But, if the direction of the wind had made an obtuse angle V C B, the sine of incidence would have augmented until the direction of the wind had been perpendicular to the sails; and it is at that moment only it would have begun to diminish, as we have shewn before.

CHAPTER VI.

OF THE EQUILIBRIUM NECESSARY TO BE KEPT IN PRACTICE, BETWEEN THE SAILS BEFORE AND ABAFT THE CENTER OF GRAVITY OF A SHIP, IN ORDER THAT THE SAILING MAY BE THE MOST DIRECT AND THE MOST RAPID.

46. AFTER having demonstrated the different effects of the sails both before and abaft the center of gravity, it is clear that if either the head or after sails only were set, in sailing by the wind, the ship would not only steer badly, but consequently sail not so fast, as she could under the same quantity of surface, differently disposed. For, if the ship be supposed (fig. 18.) to be under her head sails, and one half be retrenched and set on the masts abaft, it will evidently appear that the velocity C T they produced is the same, since the direction and the velocity of the wind act always in the same manner on the same quantity of surfaces; the only difference which will be found, is, that the primitive effect is divided, and acts now on the points C, C, E before and abaft the center of gravity of the ship. It is not the same with respect to the effect C D, which acted only the head of the vessel in the first disposition of the sails, because that effect being now divided on the after-masts, it is diminished one half C E forward, by reason of that force being transporting aft, where, balancing the effect of falling-off produced by the head-sails, it keeps the ship to the wind; by equality in the movements (§ 34 & 42.) I say that it balances, because, when the weather permits, we may at any time either increase or

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diminish the sails, so as to preserve an equilibrium between their powers, and fix the ship on her course. When this point of equilibrium is obtained, we then possess the most advantageous disposition the sails can have for the vessel to run with the greatest celerity; provided that they have been trimmed in the most favourable manner to receive (§ 28.) the greatest impulse of the wind.

This equilibrium between the powers of the sails forward and aft, is likewise advantageous with respect to the rudder; because, as there is less occasion to use it to regulate the movements of the ship, its surface opposes itself but little, and less often, to the shock of the water, which glides along the ship's bottom. It is then of the greatest importance, in endeavouring to increase the ship's way, to combine, as much as possible, the reciprocal effect of the sails fore and aft; either in setting them to the wind, or in disposing more advantageously, forward or abaft, a greater or a less quantity of sails, according as the ship is more or less inclined to fall off, or come to; in order to make as little use of the helm as possible; the whole power of which, however, at the time of performing any evolution, must be put in action, as we shall make appear hereafter.

OBSERVATIONS.

47. When there is an equilibrium between the sails fore and aft, the resistance of the water from A to B (fig. 18.) on the bows is equal to the power of the sails, whether it passes through the center of gravity H of the ship, or through another point of the axis, more or less forward or aft; then a ship, thus situated, finds no more difficulty to veer than to come to the wind, with respect to the resistance of the water under her lee; since all things are equal, viz. the resistance of the water upon the bottom to leeward, and the impulse of the wind upon the sails. But it must be considered that the power composed of those of all the sails united, acts upon the ship according to the direction B A, perpendicular to their surfaces, the origin of which is the point H, a middle between all the effects C G of the sails fore and aft, which ought to correspond exactly with the resistance of the water from A to B: so that the ship is pushed to leeward of the course I K, which she holds into the direction B A of the effort of her sails; but the resistance which she finds from the water on the lee-side of her bottom, from A to B, sets her to rights again by its opposition, which is greater by reason of the greater facility she finds in dividing the fluid with her stem, than with her side; so that she runs on the true course N R, which approaches nearer to that on which she steers than B A. Therefore the angle K H R
of the lee-way is proportional to the greater or less resistance the ship finds laterally from the fluid under her lee; which resistance depends intirely on the more or less facility she finds in dividing the water with her bows; so that the lee-way can never be considerable but when close hauled; for this reason, it is not much taken notice of when the course is less oblique than the wind on the beam. We might pursue this reasoning still further, from an experienced fact, which will prove that the lee-way depends, not only on the form of vessels, but still more on their greater or less velocity, and seldom, or never, on the intire disposition of their sails more or less oblique to the keel, as some authors have advanced. For, when a fine sailing vessel is trimmed sharp, with all her sails set, in a very light breeze, with which she scarcely obeys the rudder, the lee-way is considerable, though the sea be perfectly smooth. This great lee-way is made by the ship, because the vessel being only gently impelled, and with little force, the water, not being shocked with violence, offers little resistance, and she is then carried easily by her sails in the direction of their effort B A: and, if we consider the side of the ship, in the act of sailing, presenting a very great surface of sails above the water, it will visibly appear the lee-way will become still more perpendicular to the keel. But, let the

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wind begin to freshen, then the rapidity of sailing augments considerably; the ship shocks the water with a force expressed by the square of six or nine knots of velocity from B to A (fig. 18.) in the space of an hour, while the water repels her effort in a contrary direction: the water repels then in the ratio of this square to the square of her full velocity, and now no longer yields with facility
(§ 4); the lee-way is suddenly diminished, and is reduced to five or six degrees, and sometimes less, if the rapidity of sailing continues to increase; if, at the very time when the ship has acquired already a very great velocity, she be kept away 12° or 15°, or even 22° 30', without altering the sails, their obliquity remaining the same, the ship should then fall off in the same proportion, according to the opinion of those who have written on the theory of the working of ships. This, notwithstanding never happens; the velocity augments, because the sails then receive the wind with a greatest sine of incidence, and thereby acquire more power, while the bows continue to be still shocked by the fluid in the same parts, and with the same sine of incidence; so that the lee-way diminishes again, because the water makes a greater resistance from the increase of velocity; and that resistance is greater on the ship's side than on her bows, which is less exposed to the shock. Whence it must be concluded that the lee-way, in the same ship, does not depend alone on the disposition of her sails, and that in different ships it is always dissimilar, from their not having the same form, or their sails not trimming equally in the same oblique courses; and because, in short, they have different velocities with the same weather, and under the same sails. Which proves, in a word, that the leeway is always in a proportion compounded of the velocity of the ship; of her form, which gives her more or less resistance on her side than on the bows; and of her sails, trimmed more or less obliquely.

To return to the consideration of the action of the water on the bottom from A to B (fig. 18. ), it must be remarked, that it acts forward, and that it must consequently contribute very much to the tendency which almost all ships have to come to the wind, whenever the after-sails are in the smallest degree more powerful than those forward: for, the shock of the water is then a power which is to be added to that of the impulse of the after-sails, since this action of the fluid is so much the stronger as it acts before the center of gravity of the ship at the point M (fig. 18.), in impelling the fore part towards the wind, which always makes ships difficult to wear, because all the effort A B of the water's resistance upon the bows is opposed to this movement, in forcing this part to windward with a very great effort. It is not therefore to be wondered at when ships veer with difficulty or slowly, especially such as have a large cut-water; because there are two forces acting one against the other, and the force which comes from the sail must surmount (§ 18.) that which comes from the water; which will always easily happen, whenever, in suppressing some of the after-sails, those forwards shall be disposed favourably enough to produce that effect; and when the rudder is used at the same time; the power of which is considerable, whether the ship goes a-head or a-stern rapidly. But if the ship, being abandoned to her own proper movements in an oblique course, had on a sudden all her sails suppressed, the vessel would come to the wind, should even the rudder never be used; because the water, acting on the fore part of her bottom more on one side than the other, impels the head to windward against the smaller resistance, until its power is entirely destroyed by the total cessation of the ship's velocity.

When the ship runs so large that the after-sails becalm part of those forward, this is again another reason for the ship having an inclination to come to the wind; for, the sails forward receive a much less impulse from the wind than in a course more oblique; because the sails abaft, by increasing in their power, prevent those forward from having as much wind as their surfaces would take, since all

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the lee parts of these sails become useless for the moment, being becalmed by the weather part of those on the main mast; so that the power of the sails forward diminishes, while that of the after-sails increases; for the sine of incidence is greater. The ship ought then, for these reasons, to have more inclination to come to the wind; but, regard must be paid to the direction of the power of the sails in general, which now approaches nearer the direction of the keel: so that the greatest part of their effort is in that direction, while their force in the lateral one diminishes.

It should be farther observed, that when the ship has as much sail as the weather will permit her to carry, that is the moment of the greatest velocity of sailing, providing that the sails having at the same time received the most favourable disposition, an exact equilibrium has also been placed between those afore and those aft, so that there should be little occasion for the use of the rudder.

APPLICATION.

48. One may readily discover, from what precedes, how to distinguish the degree of quickness with which different operations ought to be performed. For example, being obliged to run for a road-stead, the wind being large, and to let go an anchor as soon as come to it, it is evident this ought to be executed but under little sail, which should be all on the part before the center of gravity; because, in the first place, a ship has always velocity enough when she sails large; secondly, because she is to overcome the effort A B (fig. 18.) of the water which opposes her movement. If, on the contrary, being obliged to come to the wind in anchoring, as many sails as can conveniently be managed at that moment may be set, because that movement of the ship is always very quick, and as soon as the sails are taken a-back, the rapidity of the ship's way diminishes, and in a few moments entirely ceases, whereas it always augments when the ship falls off.

ARTICLE I.

REMARKS ON THE EFFECT OF THE MAIN-SAIL.

49. IN the use of the sails, attention should be paid to the effect of the main-sail, which perhaps may not be that of bringing the ship to the wind; for, if the ship be too much loaded a-stern, the center of gravity H (fig. 18.) of the ship might be abaft the main-mast, and then the direction of the effort of that sail, quitting the point C before the center of gravity, ought to make the ship fall off in lieu of keeping her up to the wind. But, for this to happen, the ship must be either very ill constructed, or very badly loaded; or, in short, there must be great error in the position of her masts. Notwithstanding the main-sail may always be made to assist the ship in veering, though the center of gravity H be (as it is almost always) before the effort C of the main-sail; yet, to do it, the effect of that sail need only be changed, by making it to pass before the center of gravity of the ship: which will suddenly happen, if, when close hauled, the main sheet be let go a-main, because the weather part of the sail being fixed forward by the tack, its effect is likewise before the center of gravity of the ship, though it has lost in that part much of its power, in becoming less exposed to the impulse of the wind; while the lee part, bellying out more, can receive a great impulsion of the wind, which will strike it more and more perpendicularly as the ship falls off with more and more rapidity. In this case, it may happen, that if the direction of the effort C G of the main-sail do

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not pass before the center of gravity H of the ship, it comes so near that point, that it may be said to have no longer the effect of an after-sail.

ARTICLE II.

OF THE RUDDER.

50. THE rudder is a machine known to all the marine world; it is supported by the sternpost, to which it is affixed by braces and pintles, which operate as hinges. It acts by means of a lever, called a tiller, which enters nearly horizontally into the ship, passing under the upper or middle deck transom; so that if, instead of leaving the rudder exactly in a right line with the keel, and as it were a prolongation of it, it be turned to one side or the other, as B D (fig. 19.), it receives an immediate shock from the water which glides along the ship's bottom, in running aft from A to B; and this fluid impels it towards the opposite side, while it continues in that situation, so that the stern, to which the rudder is confined, receives the same movement; and, the ship receiving an impulse sideways, her stern turns accordingly from B to b, on any point whatever C (§ 18.), while her head passes from A to a. It must be observed, that the water strikes the rudder obliquely, and only with that part of its motion which acts according to the sine of incidence, in impelling it in the direction N P with a force which depends not only on the rapidity of sailing, but also on the greatness of the sine of incidence: a force which is consequently in the compound ratio of the square of the greater or less velocity of the ship's motion, and of the square of the larger or smaller sine of incidence, which depends upon various circumstances. So that, if the vessel runs three or four times more swiftly, the absolute shock of the water upon the rudder will be nine or sixteen times stronger under the same angle of incidence, and will be augmented in a greater proportion, if the sine of incidence be increased. This impulsion, or, what is the same, the power of the helm, is always very feeble, when it is compared with the whole weight of the vessel; but it acts with a very long arm of a lever, which occasions it to work very advantageously in turning the ship; for the helm is fixed at a very great distance from the center of gravity G, as well as from the point C, upon which the ship is supposed to turn, with respect to the point of percussion B: and if the direction P N of the impression of the water upon the rudder be prolonged, it is evident that it will pass perpendicularly at the point R, widely distant from the center of gravity G; therefore the absolute effort of the water is very powerful. It is not therefore surprising, that this machine impresses the ship with a considerable circular movement, by forcing the stern from B to b, and the head from A to a, and even much farther, when the velocity of the ship is preserved; because the effect of the helm always keeps pace with the rapidity of the ship's way.

51. Amongst all the obliquities which may be given to the rudder, there is one situation which is more favourable than any of the others, to make it produce with more rapidity the effect of turning the ship, in order to change her course. To be convinced of this, we have only to consider that, if the obtuse angle A B D (fig. 19. ) were to be lessened, the impulse of the water on the rudder would augment, at the same time that it would more oppose the sailing of the ship, since the angle of incidence would be more open, and would present a greater surface (§ 7.) to the shock of the water, by opposing its passage more perpendicularly: but then the direction N P of the effort of the helm upon the ship would pass at a smaller distance from the center of

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gravity G towards R, and would less approach the perpendicular N L, according to which, it is absolutely necessary that the power should act with greater effect to turn the ship. Therefore, it is evident that, if the obtuse angle A B D were too much lessened, the greater shock of the water could not counterbalance the loss occasioned by the distance between the direction N P and N L, or by the great obliquity which would be given to the same direction N P of the absolute effort
of the helm with the keel A B. If, on the other hand, the angle A B D were made more obtuse, the
direction N P of the effort of the rudder would become more advantageous to turn the ship since it would approach more the perpendicular N L, and since the prolongation of N P would augment G R, by passing at a greater distance from the center of gravity G. But the rudder would then be struck too obliquely; for the angle of incidence would be more acute; so that it would only present a small part of its breadth to the shock of the water, and would of course receive but a faint impulsion. All this proves that the greatest distance G R from the center of gravity G will not counterbalance the too great obliquity of the shock of the water. Whence it must be concluded, that when the water strikes the rudder too obliquely or too perpendicularly, a great deal of the impulsion, or of the effect it should produce, is lost. Therefore, between these two extremes, there is a middle position, which must be the most favourable.

52. The diagonal N P of the rectangle I L (fig. 19.) represents the absolute direction of the effort of the water upon the rudder: N I expresses the portion of this effort which opposes the ship's head-way, or which forces her a-stern in the direction of the keel. It is easy to perceive that this portion N I of the whole power of the helm contributes little to turn the vessel; for, if I N were prolonged, it would be seen that its direction passes at a very small distance G V from the center of gravity G, and that the arm of the lever B N = G V, to which the force is as it were affixed, is at most equal only to one half of the breadth of the rudder. But, it is not so with respect to the relative force N L, which acts perpendicularly to the keel. If the first force N I is almost useless, and even hurtful, by retarding the velocity; the second N L is capable of a very great effect, since it is applied at a great distance from the center of gravity G of the ship, and acts on the arm of a lever G E, which is very long. Thus, it appears, that, between the two effects N L and N I which result from the absolute effort N P., there is one which is always opposing the ship's head-way, contributing but little therefore to the motion of her turning; whilst the other alone produces that movement of evolution, without retarding her velocity.

53. Geometricians have determined the most advantageous angle made by the helm with a line prolonged from the keel, and fixed it at 54° 44', on a presumption that the ship is not wider at her floating line than at her keel. But, as that supposition is absolutely false, since all vessels augment their breadth from the keel upwards to the extreme breadth where the floating line, or highest water-line, is terminated; it follows, that this angle is too large by a certain number of degrees. For the rudder is shocked by the water, at the height of the floating line, more perpendicularly than at the keel, since the fluid exactly follows the outlines of the bottom: so that one could almost say, that a particular position of the helm might be required for each different sine of incidence upwards from the keel. But, as a middle position may be taken between all those points, we need only consider the angle formed by the sides of the ship and her axis at the highest water-line, in order to determine afterwards the middle point, and the middle angle of incidence. It appears, from Mr. Bouguer's Traite de la Manoeuvre, Sect. I. Liv. II. that, in most ships, the angle of the rudder with the prolonged line of the keel should be made to be 46° 40'. Without following the

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calculations of that able geometrician, we shall perhaps be able to explain what: he has discussed in a more abstruse manner.

54. When it is required to turn the ship by means of the rudder, and, at the same time, keeping the head-way as much as possible, it is evident that the angle 54° 44', which some have determined
to be the most favourable with the line of the keel prolonged, is in that case too open; because the water strikes the rudder with too great a line of incidence, and which is equal to that of the angle which it makes with the line prolonged from the keel below. Above, the shock of the water is almost perpendicular to the rudder, on account of the width of the ship's sides, as has been shewn before. But if the rudder opposes the fluid by making only with the line prolonged from the keel an angle of 45° 1', the impulse, by becoming weaker will be less opposed to the ship's head-way; and the direction N P (fig. 19.) of the absolute effort of the water on the rudder, approaching nearer to the lateral perpendicular N L, will be more advantageously placed; since the prolongation of the absolute effort passes at a greater distance G R from the center of gravity G. On the other hand, experience every day shows us that ships steer well, when they do not even make the angle D B E more than 35°. If this angle be made 45°, as we require it, and then we should discompose the absolute effort N P, we have the side N I equal to the other side N L of the same square; so that the part of the total power which opposes the head-way is only equal, in this case, to that which produces the movement of rotation: instead of which, if D B E. were 54° 44', N I would become much greater than N L, in proportion to the lines of the angles which are opposed to them in the triangles P I N or P L N, and the ship would consequently lose much more of her velocity than in the first situation of the rudder, to which we shall confine ourselves, as being that which is best adapted to the generality of vessels, but which nevertheless must be occasionally altered, according as they shall make an angle more or less open with their sides a-stern.*

The angle of the rudder with the keel may always be determined with sufficient precision, by observing the rule we have prescribed (§ 28.) for the determination of the angle of the sails.

55. As the water often strikes the rudder with a very great force, the tiller has a certain length, in order to lessen the labour of the helmsman.

But, to lighten his labour still more, there is in most ships, on the quarter-deck, directly over the extremity of the tiller a vertical wheel (fig. 19.) which has the effect of a capstern, and which is connected with the tiller by means of ropes and blocks (See Practice of Rigging). So that, if the wheel be turned either one way or the other, the extremity of the tiller approaches towards one of the sides of the ship, and exposes the rudder to the shock of the fluid.

56. The longer a lever is, the more effect it has when it acts with the same power: therefore, the longer the spokes of the wheel are, in proportion to the radius of the cylinder round which the tiller rope is wound, the more advantage the helmsman will have; for, if the spokes of the wheel be three or four times longer than the radius of the cylinder, the helmsman will act with three or four times more force, since he works on a lever which is three or four times longer than the radius of the cylinder, the extremity of which is supposed to be the fulcrum of the lever on which he works. So that, if he employs a force of 30 pounds weight, he will produce an effect of 90 or 120 pounds, by the disposition of the wheel alone. On the other hand, the impulse of the water is collected in the middle of the rudder's breadth, which is very narrow, compared with the length of the tiller; therefore, the effort of the water is very little distant from the point of support,; upon which it turns: whereas the tiller forms the arm of a lever 10 or 15 times longer, which still increases the power of

* It may be taken as a general position that the most advantageous angle will always be formed between 35° and 45°,

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the helmsman in a similar proportion to that which exists between the length of the tiller and that of the lever on which the impulse of the water acts. This force is therefore 10 or 15 times stronger; and the effort of 30 pounds, which before gave the helmsman a power of 90 or 120 pounds, will become one of 900 or 1800 pounds on the rudder. This advantage proceeds from the water's acting on a very short arm of a lever, while the helmsman works on one very powerful, in comparison; and, because this lever is moved by a wheel which multiplies its force. This demonstration ought to remove all surprise at the prodigious effect of the rudder, when its mechanism is not attended to; for we have only to consider the pressure of the water, which acts at a very great distance from the center of gravity G of the ship, as well as from the point C upon which she is supposed to turn (§ 15.) and there will easily be perceived the difference which exists between the effort of the water against the helmsman, and the effect of that same impulsion against the ship. With respect to the helmsman, the water acts with the arm of a lever N B very short, of which B is the fulcrum: on the contrary, with respect to the ship, the impulse of the water is exerted in a direction N P, which passes perpendicularly at a very great distance from the center of gravity G, in acting on a very long lever E G, which renders the action of the rudder very powerful in turning the ship: so that, if in a large ship, the rudder receives an impulse from the water 2700 or 2800 pounds (as very often happens provided that the ship sail at the rate of 9 or 12 knots, and that this power, applied at E, be 100 or 110 feet from the center of gravity G) it will act upon the vessel, to turn her, with a power equal to 270,000 or 308,000 pounds, while the helmsman need not act with a greater power than 30 pounds on the spokes of the wheel.

57. It is proper to remark, that the great length which is given to the tiller, in order to facilitate the work of the helmsman, is an obstacle to the play of the rudder; since that length hinders its presenting itself sufficiently to the shock of the water to produce all the effect which might attend it. For, this inconvenience does not, in most ships, allow the angle B D E (fig. 19) to be more open than 30°; whereas it should be 45° as we have before shewn. But, as this most favourable determination has not yet come into use, and the coarse dimensions commonly given the tiller have always been followed, we shall endeavour to propose something better for practice.

It must be considered, that if the tiller were shorter, the rudder would have more play, because its extremity, in describing the arc of a smaller circle, would occasion the rudder to make an angle more open, with the keel prolonged: and this new augmentation would be so much the more advantageous, as it would approach nearer to the angle of 45°. And as, in all ships, the length of the tiller might certainly be cut a fifth shorter, or perhaps more, it is evident that, thereby, the angle of the rudder and the keel prolonged might be rendered very near 45°, which would increase its force in a proportion of nearly 3 to 5, since the square of the sine of incidence of 45° is to the square of the sine of incidence of 30° :: 5 : 3, or thereabouts. This augmentation of the impulse is often of the greatest importance, especially when ships are of a large size, as their motions are but slow on account of their length.

If the tiller be shortened, the helmsman will be obliged to employ more force in proportion to the length taken from the lever on which he works: but this loss may be repaired by the facility with which the helm will be handled, if the diameter of the cylinder of the wheel be considerably lessened, augmenting at the same time the length of its axis, without diminishing that of its spokes, which ought on the contrary to be lengthened as much as possible, and two more turns of the tiller rope should be wound round the barrel.

These forces would be still multiplied, if two sheaves were fixed in the end of the tiller, in two mortises which might be made for that propose, and which might work on an iron pin passing

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through their centers, taking care to have the end of the tiller stoutly hooped with iron, in order to strengthen it; then the tiller rope might be reeved through the blocks which are for that purpose on each side the ship, thence through the two sheaves at the end of the tiller, and the standing part to be affixed close to the blocks on each side. By these means nothing would be lost with respect to the force; because if the lever be shorter, the forces which cause its action are likewise multiplied in proportion.

58. after what has been said respecting the helm, it is easy to conceive, that the greater the ship's velocity is, the more powerful is the action of the rudder, since it acts against the water with a force which increases as the square of the velocity of the fluid (§ 3.) whether the ship has head-way, or stern-way; observing always, that in these two circumstances the effects are contrary; for, if the ship goes a-stern, the rudder will be struck from I to N (fig. 19.); and, instead of being pushed from N to P, it will be so from N to R; so that the stern being moved in the same direction, the head will take a contrary one, and move towards the same side as the tiller B F.

59. It should be observed, in the use of the rudder, that there is one part of its effort which impedes the ship's sailing when it is struck by the water which runs rapidly along the ship's bottom. If it makes an angle of 45° with the keel prolonged, it receives only half the impulsion it would if acted upon perpendicularly; because the absolute impulse diminishes from two causes: (§ 7.) The surface which opposes the shock of the water is reduced to a less extent than it was at first, and the angle of incidence diminishes likewise: so that by this, the impulse has diminished one half. Considering next, that the impulsion N P, which remains (fig. 19.) it will appear that there is only one part N I which is opposed to the sailing (§ 54), and which is less than N P in the proportion as the sine total is to the sine of 45° the measure of the angle of incidence V N B equal to N P I; for the angle V N L is right, as well as the angle P N B; so that, if you take away the common angle L N B, the two angles P N L and V N B will remain equal between themselves; but, as the angle I P N is equal to its alternate angle P N L, it follows that I P N is always equal to V N B, whether the angle made by the rudder be more or less open with the keel prolonged. So that, if the surface of the rudder which receives the shock be 80 feet square superficies, it will first be reduced, by its being exposed to the course of the fluid, to an effort of 40 feet surface, then to 28 or 29, because, in the first place, there is only one part of the velocity of the water which contributes to the shock, and that is proportional to the relation of the square of the sine total to that of the sine of incidence; and, secondly, because out of the absolute impulse N P, which results from this last oblique shock, there is only a part N I which opposes the velocity of the ship proportional to the absolute N P, in the same relation as there is between the sine total and the sine of incidence; that is to say, that when the rudder makes, in the largest ships an angle of 45° it impedes the ship's rapidity of sailing, in the direction of the keel, with an effort N I equivalent to the impulsion which a surface of 28 or 29 feet square might receive if it were exposed perpendicularly to the shock of the water. So that, if the ship sails 12 knots an hour, or 19 feet a second, the effort of the rudder N I, which opposes the ship's way, will be 12,499 or 12,945 pounds; salt water weighing 1/35th more than fresh.

60. It follows, from all that has been said of the rudder, that it ought to be employed as little as possible; that is to say, the ship and her sails ought to be so disposed, that the smallest motion of this machine may bring her to her course, if she deviates from it, or make her perform any evolution which may be thought proper.

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ARTICLE III.

THE TIME EMPLOYED BY DIFFERENT VESSELS TO PERFORM THE SAME EVOLUTION, IS PROPORTIONED TO THEIR LENGTHS.

61. ALL that serves to produce motion in ships, has more force in large than in small ones; but the difficulty which large ships have to receive the motion, is greater, in a greater proportion, than that which opposes the motion of small ships. For, if the dimensions and machines which compose a large vessel, are twice as large as those which constitute a small one, (solidities being in ratio of their cubes,) the first will be eight times as great. Yet the obstacle which the large will oppose to its being put in motion will be two and thirty times as great as that of the small one. For, if both ships were considered as divided into an equal number of vertical sections, those of the large would appear to have four times as much surface as those of the small, besides that they would be twice as thick, since the dimensions are in general twice as large; consequently they will have eight times the solidity; which answers already to the relative effort of the rudder and sails.

Further, the parts of the large ship are twice as distant from the center of gravity as those of the small one, since those distances are proportional to the other simple dimensions of the two ships, So that if the evolution be supposed of the same number of degrees, the stern and head of the large ship will have to describe arcs twice as large as the small one; and this greater velocity being multiplied by the solidity of the parts of the large ship, which is eight times as great as that of the small one, the product will give 16 times more motion; the resistance will act consequently 16 times as much on the large as on the small; and as that resistance operates on the arm of a lever twice as long, the total resistance of the large ship will be 32 times as great. Thence it follows, that if the forces which act on the large ship be augmented only in proportion to her solidity, she will have still four times more difficulty than the small one to get into motion: and therefore the large ship, instead of making in the same time an angle of rotation as great as the small one, will only make an angle of one fourth, or three times less. Now, that the great ship should describe an angle of rotation equal to the other vessel, it will require only thrice as much time: but that angle, or the velocity with which the ship obeys the impulse of her rudder and sails, will follow the laws of acceleration, since the velocity acquired in the first instant is continually augmenting in arithmetical progression; so that the time which similar vessels of different sizes take in performing the same evolution, will be in proportion to their lengths. But the heavier body parts with its velocity not so readily as the lighter body, because the resistance of the mass is greater, being three times heavier than that of the small ship; which being moved with thrice the facility, is also brought to rest with the same degree of ease. So that, if a vessel 100 feet long takes four minutes to perform an evolution, a similar vessel of 150 feet will take six minutes or thereabouts to perform the same circular movement. For as 100:150 :: 4:6.

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CHAPTER VII.

OF THE HEIGHT OF MASTS.

THE correct height for the masts of ships is still a problem which remains to be solved for the builders. The most skilful of them have not paid attention enough to the solutions and determinations which are contained in the Works of the late Mr. BOUGUER on that subject. It seems, on the contrary, as if they had endeavoured to deviate, as much as possible, from the true principles in that respect, by raising the masts a great deal more than they were formerly, although they were already much too high, as the learned Author I have just mentioned has asserted. An experience, confirmed by repeated observations, has convinced me of this truth; viz. that "as soon as a ship inclines, her velocity diminishes in proportion as her inclination increases." This principle has been verified on different vessels, and at different times by several officers; and in various oblique courses. I had no share in those various experiments, and therefore cannot be suspected of partiality: but, as they have always proved, to those who have made them, that the present mode of masting is generally too high, I will not hesitate a moment longer to deliver here an epitome of my own experiments on that subject.*

Having all the sails out, and being hurried on by a strong gale, I have ordered all the top-gallant-sails, the studding and stay sails, to be taken in, without the ship losing the least perceptible degree of her velocity; nay, I have seen it sometimes to increase by a twentieth, and that at a time when the ship ran already at the rate of nine or twelve knots an hour.

These trials, which I have made with care, and which were performed so quickly, that the wind should not have time to increase or diminish in strength, are sufficient to prove the necessity of lowering the center of effort of the sails in general, and consequently all the masts. These experiments have been repeated in augmenting the number of sails, sometimes at the risque of fatiguing the masts; and it has always been found that the velocity did not increase, when the ship was more inclined; but that she laboured more and more in all her parts, as her movements became stronger and the concussions of her pitchings rougher, although the sea was not more swelled. At other times, when the ship inclined pretty much, though the wind was not quite strong enough to hurt the masts, I have lessened the number of sails; and it happened that the ship, after that suppression of the top-sails, was easier in her movements, steered better, and was, in short; more quiet, though the swells of the sea were still the same; an attention which must not be neglected in these kinds of observations, which should be often repeated before a positive decision. However, we do not recommend any diminution in the surface of the sails, in lessening their height: but, it will often happen that we shall rather recommend to increase it upon the whole. For that which is lost in height, may be regained by the width. There will even result, from that operation, another advantage: the top-sails, by this reform, being shorter and, thereby, proportionally wider than the lower sails, will be more easily cut to their shape; and their sides being formed with lines exactly strait, the sail will be the more tight, by which a much greater effect on the ship will be produced. The masts being shorter, and the sails

* We have thought it proper to give the reasoning of M. Bourde upon this subject although the practice of high-masting prevails in the British Navy.

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wider, with less fall, the surface will be the same: but the effort of that surface will, with the same wind, act on shorter levers, the fulcrum of which will not be altered; therefore, it will operate at a shorter distance from that fulcrum; and therefore much less will be the power which makes the ship incline: and the ship, being more upright, will sail with more velocity, because her water-lines will be then more advantageous than when she heels. On the other hand, the sails being less inclined, they present a wider surface to, and receive a stronger impulsion from, the wind; an advantage which must always produce an increase of swiftness and a decrease of drift. Add to this the real advantages of trimming the sails better, of working them with more ease, of rendering the masting in general more solid, and more capable of resistance in bad weather, as well as in battle.

But, how must we determine the height for the masts? or, in other words, how much they are to be shortened? The Treaties on the perfect masting and working of ships, by M. BOUGUER, teach us that method. It is from those Treatises I have imbibed the notions of my principles on that subject. But, in order to give a previous idea of that inquiry, and to engage the builders and seamen to bring to perfection this part both of the building and working of ships; upon which, almost as much as from their bottom, their steerage undoubtedly depends, I will subjoin here what M. BRUE, a learned and studious Officer, made me conceive on that subject.

"That masting," said he, "is absolutely perfect, when the center of effort of the sails is precisely opposite to, or at the same height as, or parallel with, the point velique. What is the point velique ? It is that point in a perpendicular, (raised from the center of gravity of the horizontal surface of the ship at the floating line,) which is intersected by the direction of the absolute impulse of the sea on the head of the vessel. This is the point-velique in direct courses."

It is clear; no great effort of imagination is necessary to conceive this principle, which appears so evident, that it may be surprising why it has not yet been made use of. For this point once known, the center of effort of the sails will be so too; and their right height, as well as that of the masts, will be determined. A little more calculation, and an attention to the plan of the ship will be necessary, in order to find out that absolute direction of the effort of the impulsion of the water on the bows. But that should not prevent the enquiry. On the contrary, it should be an additional inducement to those who, building such good vessels as we are now possessed of, and which might still be of a more advantageous form, will be desirous to make them more perfect, by masting them more advantageously. This would undoubtedly be the case; for several vessels have had their masts cut shorter, and the practice has been attended with decided success. These facts, which could be attested by many able seamen, will always speak highly in favour of this principle; although, when that shortening was made, the sails were not widened in proportion.

"But," continues M. BRUE, "in carrying this inquiry farther than it ever was, the intersection
of the two above-mentioned lines, (viz. that of the absolute impulse of the water on the bows, and
that of the perpendicular at the center of gravity of the surface of the floating line of the ship,)
cannot take place unless in a direct course; and, as soon as the course becomes oblique, they no
longer meet. The center of gravity of the floating line's surface of the ship passes to the leeward of its axis, on account of the inclination which always occurs in that sort of course; and the
direction of the shock of the fluid, which then takes its origin a little to leeward also of the bow,
passes, in its prolongation, to windward, without meeting the perpendicular at the center of gravity of the floating line's surface;" (which is easily conceived, if we represent to our imagination
the horizontal edge of that floating line's surface but ever so little inclined;) " whence it results that

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"no point-velique will be found in any course but a direct one: which is true; unless we could fancy
such a ship as would neither drive nor incline in an oblique course: but that is not possible; and
hence no perfect mode of masting could be discovered in the last case of the oblique course."

This is true, strictly speaking: for, in each instant of a course a different point of the bow is struck by the water; which is owing to the pitching of the ship, the continual variations in the strength of the wind, and the greater or smaller inclination produced by the rolling motion of the ship.

"But," says again M. BRUE, " the point-velique, relative to these various circumstances, varies
therefore in the proportion of the almost infinite variety of those circumstances, which accompany
the course of a ship, that is to say, according to all the degrees of drift, all the degrees of inclination on either board, forward or abaft; as many times, in short, as there are new points of the
bow either struck, or no longer struck, the point-velique ascends or descends.

"I pass over the minute examination I could make of each particular cause which contributes to
lower that point from its utmost height, which is in the direct course, to its lowest, which takes
place in the most oblique course, accompanied with the greatest lateral inclination of the ship: and
there is no method to get out of that common road which is pursued in determining the
dimensions of the masts, but that of attending to the following considerations; viz. Such a ship
being intended for such a latitude, the wind she is most commonly to expect there, will be nearly
of such a strength, and generally oblique to her course by so many degrees: so that her most common drift will be nearly so many degrees, and her lateral inclination so many, &c. To give her,
therefore, the most suitable masting, making her relatively perfect, we must seek for her point-velique
in what situation we shall think most convenient, and there place the center of effort of her
sails."

All this reasoning tends evidently to the shortening of all the masts, and proves the necessity of doing it, at the same time as it determines their height. The most difficult point, in that operation, is to find out the direction of the absolute impulsion of the water on the bows, when the ship steers a course close hauled and one with the wind on the beam, with such an inclination as the ship could be supposed to have in either of these two courses; when the wind would allow to have four square-sails set, together with the mizen top-sail. Considering these two suppositions of the wind on the beam, and close hauled, it will be easy to determine the height of the masts proper for that double situation; because, if the gale blows harder, one may lessen the number of sails; if weaker, one may increase it by adding stay-sails, top-gallant sails, jib, &c: if the wind gets more aft, then the surface of the sails may be increased again by adding the studding and top-gallant royal sails: finally, it is very clear that top-gallant and top-gallant royal sails will always be of service when the center of effort of the sails should ascend.

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CHAPTER VIII.

OBSERVATIONS ON THE DIFFERENT INCLINATIONS GIVEN To THE MASTING OF SHIPS, WITH RESPECT
TO THE WATER-LINE.

THE masts are hardly ever stepped in the same manner in all ships. This, too, is one of those things which are rather regulated by custom than reason. Some will have them perpendicular, while others chuse to have them rake forward, and others aft. Each party bring, to support their opinion, reasons drawn from some experiments which chance has sometimes rendered specious.

In this respect, we should rely on the judgement of the builder, who ought to know the qualities of his ship even before he puts her on the stocks. If one has not an opportunity of taking directly from him the necessary instructions, it is proper to observe that, if the masts are made to rake forward, the direction of effort of the sails will be inclined towards the bottom, obliquely with the horizon; which will consequently make the head of the ship plunge whenever they receive a strong impulse from the wind; and this may diminish the head-way of the ship, while it increases the celerity of the pitching: the sails also will be with more difficulty trimmed, especially when close hauled, since the bracing of the yards will be more confined. Therefore, the only advantage which can be drawn from this oblique masting of ships, is only to render the ships more ready to fall off.

If the masts are perpendicular the direction of effort of the sails will be horizontal, always supposing the ship to be in an upright position. Therefore, this effort not being discomposed, it will preserve a much greater action, and the ship will sail with the greatest velocity she is capable of.

If the masts rake aft, the ship will be more ready to come to the wind, because the sails will be a little more aft: these will also be more easy to trim sharp because the braces will not be so much confined. As this position of the sails will raise obliquely above the horizon the direction of the effort on the ship, it follows that, by their power, the ship will be eased away from the water: for, it is certain that she will not prolong her course, unless she heels too much; therefore, she will rise more lightly over the waves, pitch less, keep better the wind, and tack quicker. This is nearly all that can be said in respect to practise.

CHAPTER IX.

OF THE TENSION OF SAILS, AND THEIR TENDENCY TO FIX THEMSELVES PERPENDICULARLY TO THE
DIRECTION OF THE WIND.

I. IT is clear that sails are never perfectly flat. But every one is not persuaded that the more extended is the sail, the greater impulsion it receives from the wind, which strikes it perpendicularly, and the more effectually, of course, the sail acts on the vessel. It is astonishing that any seamen should be of opinion that a bag must be left at the foot of the sail, to lodge the wind in. A hauled-

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down top-sail has as much cloth displayed in it as when hoisted up and well extended. It forms then, by its convexity, a considerable kind of bag, in which the wind may play at ease; and it is observed that the rapidity of the sailing decreases very much; whence we must necessarily conclude, that the impulse of the wind must have greatly diminished, since the sail produces no longer the same effect upon the vessel. To know demonstratively the cause of that diminution in the impulse of the wind, we have only to pay attention to the air which acts against the foot and the head of the sail; for that part of the wind, which strikes at the head, makes an effort to re-act towards the foot against that which, having struck at the same instant at the foot, endeavours to re-act towards the head. From this shock results (though the air escapes at each side) a compression in the sail. But, after having acted inwardly in the same manner as if it were shut up, it finds itself more and more compressed by that which succeeds to the first; and, though it escapes by the sides, it is evident that it tries to extend, and that it impels consequently with an equal power, all the parts of the sail perpendicularly; and this is the cause of the sail taking the form of a circle's arc. Therefore the sail will produce no greater effect than if it had no greater height than the space contained between the two yards: it may not even, strictly speaking, have that whole effect; for, that sort of whirlwind, which is made in the center, by the re-action of the wind which strikes the upper and lower parts, cannot fail to diminish the shock of those particles, which succeeding the former, would have struck the sail with all their primitive power; instead of which, this power is now almost intirely destroyed by this barrier which opposes for a while their passage. To which may be added, that the sail having the form of the arc of a circle, very little wind can strike it perpendicularly; and that it must, of course, have much less effect than another sail, of the same height and width, which should be very exactly stretched out.

The sails of a ship should be cut in such a form, as to present as flat a surface as possible.

II. The center of effort of the impulse of the wind upon the sails, exposed perpendicularly to the course of the wind, answers exactly to the center of gravity of the surface, struck in that direct situation. But, as soon as it is presented obliquely to the course of the fluid, and kept so, the center of effort of the total impulse will pass on the weather side of its center of gravity; because the particles of air which at first met the surface, have been re-acted, and by that re-action, they stop part of the passage to the succeeding ones, which diminishes of course both the strength of the shock and the impulse they would have communicated to the sail, if their movement had not been interrupted. But, this deviation of re-action in the first particles of air which have struck, is repeated afterwards. For, all those which succeed them while the surface is kept obliquely to the wind, continue to re-act to leeward: so that, from the first vertical line (taken from the windward side) out of all those which form together the surface, there is a continual series of obstacles which change the shock of immediate and succeeding particles, and which alters it so much the more as they ought to strike the parts of the sail most to leeward, and so much the less as they will strike those which are most to windward. Therefore, the leeward side of sails, obliquely exposed to the wind, is always less struck than that which stands to windward. Whence it results that the center of effort of the absolute impulse of the wind on the sail, is lodged in the weather side of the sail, (for it is supposed to be equally divided in two,) since that is the part which receives more impulsion. Therefore, the center of effort is also to windward of the center of gravity of the surface; and the removal of this center of effort towards the wind, is in proportion to the impulse received on the weather side of the sail, and that received on the lee side. The truth of this assertion is continually demonstrated by daily experience of ships at sea. The sails are carried by the yards and by the masts, which divide them perpendicularly into two equal parts, from top to bottom, through their center of gravity. When, being placed obliquely to the wind, they are left at liberty, without being confined by their braces or bowlines, they immediately range themselves

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perpendicularly to the course of the wind, because their weather side receives more impulse than the lee side; and there they remain constantly, unless their position be altered; because all their parts are struck equally, and an equilibrium is kept among them; for, the power of the wind, whether it increases or decreases, acts always the same on them all.

This proof, which shews the difference between the center of gravity and the center of effort in the sails, requires much attention in the use of that knowledge in practice. For example, in the middle of the yards on their aft side, there might be fixed a cleat, or bolster, which, in oblique courses, pushing them to leeward, would ease them off from the shrouds, and facilitate their bracing in carrying their center of gravity, as well as the center of the absolute effort, a little to leeward; which operation would of course draw that center of gravity nearer to the axis of the ship, from which it is so essential to remove it as little as possible.

CHAPTER X.

GENERAL OBSERVATIONS ON THE EFFECT OF MORE OR LESS SURFACE OF SAILS EXPOSED, IN VARIOUS
WEATHERS, To THE WIND.

I. WHEN a ship, with a certain quantity of sail has acquired the utmost velocity with the power which then puts her in motion, it is certain that, if the surface of the sails is either increased or diminished, the rapidity of the head-way will likewise augment or lessen in a very complicated ratio. In order to find out the degree of impulsion of the wind on the sails, multiply their surface by the square of the excess of the velocity of the wind on that of the ship, or, which is the same thing, by the square of the apparent velocity of the wind. Then, a second multiplication of that product is to be made by the square of the sine of the angle of absolute incidence, or, in the second case, by the square of the sine of apparent incidence. And this second product will give the degree of the absolute impulse of the wind on the sails, in the actual state which we have supposed.

In order to find in what ratio the surface of the sails is to be augmented to make the ship acquire a certain degree of velocity above that which she possessed under a supposed particular quantity of sail, it must first be known by how much the velocity of the wind exceeds that of the ship: then, knowing how many degrees her head-way is wished to be accelerated, the sails must be increased in the ratio of the squares of the two velocities of the ship; viz. that which was known before the alteration of the sails, and that which she is afterwards to acquire. But, as the ship recedes so much the more from the action of the impulse of the wind as her velocity increases, it is evident the surface of the sails must be increased also in the ratio of the square of the two excesses, that is, the different excess of the wind over that of the ship both before and after the increase of the sails: then, the ship will acquire the wished-for velocity;

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provided no other cause happens to oppose it, as we have already hinted before, and as we shall have an opportunity to shew more particularly hereafter.

Suppose the wind has 12 degrees velocity, and the ship, under a certain set of sails, has 3; the velocity of the wind, in the direct course, will exceed that of the ship only by 9 degrees. If the velocity of the ship is intended to equal the third part of that of the wind, and to have therefore 4 degrees for head-way; then the sails are, to this effect, to be increased in the ratio of the squares of the squares of the two velocities 9 to 16, because the resistance of the water on the bows will increase in that very proportion. But, in the first case, the velocity of the wind exceeded that of the ship by 9 degrees, while in the second case it exceeds it no more than 8. Hence it results that the impulse of the wind on the sails has diminished in the ratio of the two squares 81 to 64: and, in order to repair that loss in the impulsion of the wind, the expansion of the sails is also to be increased in that last ratio of 64 to 81: then the ship will be able to run with the degree of velocity defined.

II. When the masting is perfect, that is to say, when the ship is masted according to the point-velique, she will rise from the water parallel to herself by a certain quantity relative to her velocity, and she will rise always more and more in proportion as she acquires new degrees of velocity in her head-way. Because she is moved by forces which stand exactly and continually in equilibrium with the action of the water on her bows, the inclination of which forward contributes so much the more to that rising out of the water as it is more remote from the perpendicular. For, then, the vertical impulsion will have more power, since it acts more directly on a very oblique bow than it would on a vertical one. This reasoning may be as exactly applied to the direct impulsion, the absolute effort of which may be decomposed, since it acts less against the velocity of the sailing on an oblique bow than on a vertical one, while the other part of its action joins with the vertical impulse to raise the head of the ship, which shocks the water with very great strength when she is arrived to a great velocity, and which water opposes her so much the more as it is shocked with violence. So it is easy to conclude that, in any ship whatever, the more rapid the head-way is the more parallel to herself she rises above the water, if the center of effort of her sails is at the same height as the point-velique: for the point of the bows, on which may be considered as united the action of the water which opposes its progress, may be taken also as the point of bearing. So that all the sails acting from abaft to forward on different points of the axis of the ship, (she being considered as a lever in the direction of her length), they raise the after part of that point, and place it on a level with the elevation of the bows; which never can happen, if the center of effort of the sails is above or below the point-velique. If it is placed above, the power of the sails, acting on too long levers, will raise the after part of the point of bearing of the bows above the level of the elevation of the ship's head. If it is placed below, the power of the sails, acting on too short levers, the after part of the ship will remain plunged in the water, without being able to rise on a level with the bows. Therefore, in either of the two cases, when the center of effort of the sails is either above or below the point-velique, the ship, however well-built, will lose some of the qualities of sailing, either in her readiness to obey the helm, or in her steadiness to carry sail, especially if she is over-masted: for, in this last case, she will gripe, incline easily, and lose much of her head-way, since her bows will plunge in the fluid, or, rather, her stern will rise too much out of it; which will diminish; the action of the water on the rudder and increase it on the bows. In the last case, an inconvenience of which ship builders seldom, if ever, have been guilty, the ship will be slow to obey, and her head-way will be slackened, because she will never present her most advantageous water-lines to the fluid, nor have a sufficient

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surface of sails, as, although their width is the same, their height is not so. The point of perfection then is this, viz. when the center of effort of the sails is placed at the height of the point-velique.

III. The next proposition will appear a paradox to many seamen. But, it is no less self-evident.

There are many cases in which the adding of a few sails, instead of increasing a ship's velocity, retards it. It is however an error into which all seamen almost continually fall, when, in a strong gale, they want either to distance, or approach a ship. When their own ship is arrived to a very great velocity (sometimes of twelve and more knots an hour), if they have to do with an adversary the rapidity of which is nearly equal to that of their own ship, they fancy that, by adding more sails to those they have already, at the time when their ship is perhaps best disposed and arrived at its utmost degree of swiftness, they shall increase the rapidity of her head-way; and, accordingly, they hoist up some additional stay or studding sails, especially if the wind happens to be on the beam or a little more aft. But, by this their expectations are baulked; for the ship becomes more inclining, her head plunges, and the resistance of her bows increasing in the direction of the keel more than the effort of the sails in the direction of the course, the rapidity decreases in so much as the water acts more powerfully than the sail does. Besides all this, those forward and lateral inclinations of the ship, produced by the effort of the new-added sail, which have caused the center of effort of the sails to ascend, and the point-velique to descend (if the new-added sail has been set above it), cause also the ship not to rise from the water parallel to herself; she rises her stern and plunges her head; whence it results that she gripes from two causes: first, because, as her stern lies less in the water, the rudder is of course exposed to a less shock; and the stern, which always acts as a sail, is more easily mastered by the wind which strikes it then on the beam with a great deal more efficacy than it does her head; on the other hand, as the resistance of the water on the lee bow has increased by the inclining of the head, plunging thereby that part of the ship which is the most full in its shape, and increasing also the surface on which the water acts, which has both diminished the head-way and increased at the same time the lateral impulse on the side of the bow; so that lateral impulsion forces the ship to windward more at the head, than she is impelled to fall off by the lateral part of the effort of the new-added sail. Whence it follows that the ship becomes still more griping, which is an additional cause of the decrease of her head-way; because, the helm being more a-weather, in order to hold the ship better to her course, more of the rudder itself is presented to the run of the water; and by the great surface it offers more directly to its shock, and retards the velocity of the ship. Whence we are to conclude that as soon as any more sails are added to a ship which carries already a sufficient quantity of them, she will lose her qualities of steering well and making good head-way, whether those additional sails are set forward or a-stern.